3. Performance analysis

#### 3.1 Outage probability

Outage probability is an important performance metric for system designers [12]. It is generally used to characterize a wireless communication system and defined as the probability that the instantaneous end-to-end SNR (γe2e) falls below the predetermined threshold <sup>γ</sup>th (γth = 2Ω�1, where <sup>Ω</sup> is fixed transmission rate at the source), given by

$$P\_{\rm out} = \Pr(\chi\_{e2\varepsilon} < \chi\_{th}).\tag{18}$$

In this considered system, the outage event at the destination occurs when Dm cannot detect successfully sn or sm or when Dm can detect successfully sn and sm, but an outage occurs in information relaying phase. Accordingly, outage probability of this RF-EH NOMA relaying system is written as

$$\begin{split} P\_{out} &= \Pr\left(\boldsymbol{\chi}\_{\text{SD}\_m}^{\boldsymbol{\epsilon}\_n} < \boldsymbol{\chi}\_{th}\right) + \Pr\left(\boldsymbol{\chi}\_{\text{SD}\_m}^{\boldsymbol{\epsilon}\_n} > \boldsymbol{\chi}\_{th}, \boldsymbol{\chi}\_{\text{SD}\_m}^{\boldsymbol{\epsilon}\_m} < \boldsymbol{\chi}\_{th}\right) \\ &+ \Pr\left(\boldsymbol{\chi}\_{\text{SD}\_m}^{\boldsymbol{\epsilon}\_n} > \boldsymbol{\chi}\_{th}, \boldsymbol{\chi}\_{\text{SD}\_m}^{\boldsymbol{\epsilon}\_m} > \boldsymbol{\chi}\_{th}\right) \Pr\left(\boldsymbol{\chi}\_{\text{D}\_n}^{\boldsymbol{\epsilon}\_n} < \boldsymbol{\chi}\_{th}\right). \end{split} \tag{19}$$

Notice that because the messages are transmitted in the duration of (1�α)T/2, thus <sup>γ</sup>th is calculated by <sup>γ</sup>th = 22Ω/(1�α) � 1, where <sup>Ω</sup> is fixed source transmission rate.

Substituting Eqs. (6), (7), and (13) into Eq. (19), we obtain the following equation:

$$\begin{split} P\_{out} &= \Pr\left(\frac{b\_2 X\_2}{b\_1 X\_2 + 1} < \gamma\_{th}\right) + \Pr\left(\frac{b\_2 X\_2}{b\_1 X\_2 + 1} > \gamma\_{th}, \ b\_1 X\_2 < \gamma\_{th}\right) \\ &+ \Pr\left(\frac{b\_2 X\_2}{b\_1 X\_2 + 1} > \gamma\_{th}, \ b\_1 X\_2 > \gamma\_{th}\right) \Pr(c\_1 X\_1 X\_3 < \gamma\_{th}) \\ &\times \left[ \Pr(b\_3 Y\_2 < \gamma\_{th}) + (1 - \Pr(b\_3 Y\_2 < \gamma\_{th})) \Pr\left(\frac{c\_2 Y\_1 Y\_3}{c\_3 Y\_3 + 1} < \gamma\_{th}\right) \right] \\ &= I\_1 + I\_2 + I\_3 I\_4 [I\_5 + (1 - I\_5) I\_6], \end{split} \tag{20}$$

where

$$I\_1 = \Pr\left(\frac{b\_2 X\_2}{b\_1 X\_2 + 1} < \gamma\_{th}\right),\tag{21}$$

$$I\_2 = \Pr\left(\frac{b\_2 X\_2}{b\_1 X\_2 + 1} > \gamma\_{th}, \ b\_1 X\_2 < \gamma\_{th}\right),\tag{22}$$

$$I\_3 = \Pr\left(\frac{b\_2 X\_2}{b\_1 X\_2 + 1} > \gamma\_{th}, \ b\_1 X\_2 > \gamma\_{th}\right),\tag{23}$$

$$I\_4 = \Pr(\mathcal{c}\_1 X\_1 X\_3 < \gamma\_{th}),\tag{24}$$

$$I\_5 = \Pr(b\_3 Y\_2 < \chi\_{th}),\tag{25}$$

Performance Analysis for NOMA Relaying System in Next-Generation Networks with RF Energy… DOI: http://dx.doi.org/10.5772/intechopen.89253

$$I\_6 = \Pr\left(\frac{c\_2 Y\_1 Y\_3}{c\_3 Y\_3 + 1} < \gamma\_{th}\right). \tag{26}$$

By the help of Eqs. (14)–(17), we obtain the exact closed-form expressions of I1, I2, I3, I4, I5, and I6, respectively, as follows:

I<sup>1</sup> ¼ 1, γth> an am FX<sup>2</sup> γth <sup>b</sup><sup>2</sup> � <sup>b</sup>1γth � �, <sup>γ</sup>th <sup>&</sup>lt; an am 8 >>>< >>>: ¼ 1, γth> an am : M! ð Þ M � m !ð Þ m � 1 ! Xm�1 k¼0 C<sup>m</sup>�<sup>1</sup> <sup>k</sup> ð Þ �<sup>1</sup> <sup>k</sup> M � m þ k þ 1 1 � e �ð Þ <sup>M</sup>�mþkþ<sup>1</sup> <sup>γ</sup>th <sup>λ</sup><sup>3</sup> <sup>b</sup>2�b1γth ð Þ � �, <sup>γ</sup>th <sup>&</sup>lt; an am : 8 >>>< >>>: (27) I<sup>2</sup> ¼ FX<sup>2</sup> γth b1 � � � FX<sup>2</sup> γth <sup>b</sup><sup>2</sup> � <sup>b</sup>1γth � �, <sup>γ</sup>th <sup>&</sup>lt; an am � 1 0, γth> an am � 1 8 >>>< >>>: ¼ M! ð Þ M � m !ð Þ m � 1 ! Xm�1 k¼0 C<sup>m</sup>�<sup>1</sup> <sup>k</sup> ð Þ �<sup>1</sup> <sup>k</sup> M � m þ k þ 1 e �ð Þ <sup>M</sup>�mþkþ<sup>1</sup> <sup>γ</sup>th <sup>λ</sup><sup>3</sup> <sup>b</sup>2�b1γth ð Þ � e �ð Þ <sup>M</sup>�mþkþ<sup>1</sup> <sup>γ</sup>th <sup>λ</sup>3b<sup>1</sup> � �, <sup>γ</sup>th <sup>&</sup>lt; an am � 1: 0, γth> an am � 1: 8 >>>< >>>: (28)

$$I\_{3} = \begin{cases} 1 - F\_{X\_{2}} \left( \frac{Y\_{th}}{b\_{1}} \right), & \gamma\_{th} < \frac{a\_{n}}{a\_{m}} - 1 \\\\ 1 - F\_{X\_{2}} \left( \frac{Y\_{th}}{b\_{2} - b\_{1} \gamma\_{th}} \right), & \frac{a\_{n}}{a\_{m}} - 1 < \gamma\_{th} < \frac{a\_{n}}{a\_{m}} \\\\ 0, & \gamma\_{th} > \frac{a\_{n}}{a\_{m}} \end{cases}$$

$$= \begin{cases} 1 - \frac{M!}{(M-m)!(m-1)!} \sum\_{k=0}^{m-1} \frac{C\_{k}^{m-1}(-1)^{k}}{M - m + k + 1} \left[ 1 - e^{\frac{-(M-m+k+1)\gamma\_{th}}{b\_{1}\gamma\_{th}}} \right], & \gamma\_{th} < \frac{a\_{n}}{a\_{m}} - 1 \\\\ 1 - \frac{M!}{(M-m)!(m-1)!} \sum\_{k=0}^{m-1} \frac{C\_{k}^{m-1}(-1)^{k}}{M - m + k + 1} \left[ 1 - e^{\frac{-(M-m+k+1)\gamma\_{th}}{b\_{1}(\gamma\_{th}-b\_{1}\gamma\_{th})}} \right], & \frac{a\_{n}}{a\_{m}} - 1 < \gamma\_{th} < \frac{a\_{n}}{a\_{m}} \\\\ 0, & \gamma\_{th} > \frac{a\_{n}}{a\_{m}} \end{cases} \tag{29}$$

:

$$I\_4 = \Pr\left(X\_3 < \frac{\chi\_{th}}{c\_1 X\_1}\right) = \bigcap\_{0 \atop \lambda\_1 \lambda\_3 \in \Lambda\_1}^{\infty} \left(\frac{\chi\_{th}}{c\_1 \mathfrak{z}}\right) f\_{X\_1}(\mathbf{z}) d\mathbf{z} = \int\_0^\infty \left(1 - e^{-\frac{\gamma\_{th}}{4\mathfrak{z}\chi\_1\mathfrak{z}}}\right) \frac{1}{\lambda\_1} e^{-\frac{\tilde{\chi}}{4\mathfrak{z}}} d\mathbf{z} \tag{30}$$

$$= 1 - 2\sqrt{\frac{\chi\_{th}}{\lambda\_1 \lambda\_3 \varepsilon\_1}} \mathbf{K}\_1 \Big(2\sqrt{\frac{\chi\_{th}}{\lambda\_1 \lambda\_3 \varepsilon\_1}}\Big). \tag{31}$$

$$I\_5 = 1 - e^{-\frac{\gamma\_{th}}{4\mathfrak{z}\chi\_3}}. \tag{32}$$

FVð Þ¼ x 1 � e

Outage probability is an important performance metric for system designers [12]. It is generally used to characterize a wireless communication system and defined as the probability that the instantaneous end-to-end SNR (γe2e) falls below the predetermined threshold <sup>γ</sup>th (γth = 2Ω�1, where <sup>Ω</sup> is fixed transmission rate at

In this considered system, the outage event at the destination occurs when Dm cannot detect successfully sn or sm or when Dm can detect successfully sn and sm, but an outage occurs in information relaying phase. Accordingly, outage probability of

> þ Pr γ sn SDm >γth, γ

> > sm SDm >γth

Notice that because the messages are transmitted in the duration of (1�α)T/2, thus <sup>γ</sup>th is calculated by <sup>γ</sup>th = 22Ω/(1�α) � 1, where <sup>Ω</sup> is fixed source transmission rate. Substituting Eqs. (6), (7), and (13) into Eq. (19), we obtain the following

b1X<sup>2</sup> þ 1

<sup>b</sup>1X<sup>2</sup> <sup>þ</sup> <sup>1</sup> <sup>&</sup>lt;γth 

>γth, b1X<sup>2</sup> <γth

>γth, b1X2>γth

I<sup>4</sup> ¼ Pr c1X1X<sup>3</sup> <γth ð Þ, (24) I<sup>5</sup> ¼ Pr b3Y<sup>2</sup> <γth ð Þ, (25)

<sup>þ</sup> Pr <sup>b</sup>2X<sup>2</sup>

>γth, b1X2>γth

� Pr <sup>b</sup>3Y<sup>2</sup> <sup>&</sup>lt; <sup>γ</sup>th ð Þþ <sup>1</sup> � Pr <sup>b</sup>3Y<sup>2</sup> <sup>&</sup>lt;γth ð Þ ð Þ Pr <sup>c</sup>2Y1Y<sup>3</sup>

<sup>I</sup><sup>1</sup> <sup>¼</sup> Pr <sup>b</sup>2X<sup>2</sup>

b1X<sup>2</sup> þ 1

b1X<sup>2</sup> þ 1

<sup>I</sup><sup>2</sup> <sup>¼</sup> Pr <sup>b</sup>2X<sup>2</sup>

<sup>I</sup><sup>3</sup> <sup>¼</sup> Pr <sup>b</sup>2X<sup>2</sup>

where λ ∈ {λ1, λ2, λ4, λ5, λ6}.

Recent Wireless Power Transfer Technologies

this RF-EH NOMA relaying system is written as

Pout ¼ Pr γ

<sup>b</sup>1X<sup>2</sup> <sup>þ</sup> <sup>1</sup> <sup>&</sup>lt;γth 

¼ I<sup>1</sup> þ I<sup>2</sup> þ I3I4½ � I<sup>5</sup> þ ð Þ 1 � I<sup>5</sup> I<sup>6</sup> ,

b1X<sup>2</sup> þ 1

sn SDm <γth 

þ Pr γ sn SDm >γth, γ

3. Performance analysis

3.1 Outage probability

the source), given by

equation:

where

110

Pout <sup>¼</sup> Pr <sup>b</sup>2X<sup>2</sup>

<sup>þ</sup> Pr <sup>b</sup>2X<sup>2</sup>

�x

<sup>λ</sup> , (17)

Pout ¼ Pr γ<sup>e</sup>2<sup>e</sup> <γth ð Þ: (18)

sm SDm <γth

>γth, b1X<sup>2</sup> <γth

<sup>c</sup>3Y<sup>3</sup> <sup>þ</sup> <sup>1</sup> <sup>&</sup>lt;γth

, (21)

, (22)

, (23)

: (19)

(20)

Pr γ sn Dn <γth 

Pr c1X1X<sup>3</sup> <γth ð Þ

$$\begin{split} I\_{6} &= \Pr\left(Y\_{3} < \frac{c\_{3}\chi\_{th}}{c\_{2}}\right) + \Pr\left(Y\_{3} < \frac{\chi\_{th}}{c\_{2}Y\_{1} - c\_{3}\chi\_{th}}, Y\_{1} > \frac{c\_{3}\chi\_{th}}{c\_{2}}\right) \\ &= F\_{Y\_{3}}\left(\frac{c\_{3}\chi\_{th}}{c\_{2}}\right) + \int\_{\begin{subarray}{c} c\_{3}\chi\_{th} \\ c\_{2}\end{subarray}}^{\infty} F\_{Y\_{3}}\left(\frac{\chi\_{th}}{c\_{2}\varpi - c\_{3}\chi\_{th}}\right) f\_{Y\_{1}}(z) dz \\ &= 1 - 2e^{-\frac{c\_{3}\chi\_{th}}{c\_{2}\chi\_{2}}} \sqrt{\frac{\chi\_{th}}{\lambda\_{2}\lambda\_{6}c\_{2}}} \mathbf{K}\_{1}\left(2\sqrt{\frac{\chi\_{th}}{\lambda\_{2}\lambda\_{6}c\_{2}}}\right). \end{split} \tag{32}$$

Parameters System values Environment Rayleigh Number of antennas of each node 1 Fixed rate (Ω) 1 bps/Hz Number of users (M) 4, 6, 8 Energy conversion efficiency (η) 0.9 Distances (d) 1 Path loss exponent (θ) 2

Performance Analysis for NOMA Relaying System in Next-Generation Networks with RF Energy…

Pout vs. average transmit SNR of P with different numbers of users M with γ<sup>S</sup> = 20 dB, an = 0.9, m = 2, n = 3,

Throughput Φ vs. average transmit SNR of P with different numbers of users M with γ<sup>S</sup> = 20 dB, an = 0.9, m = 2, n = 3, Ω = 1 bps/Hz, α = 0.3, η = 0.9, dPDm = dPR = dSDm = dSR = dmn = dRDn = 1, θ = 2.

Ω = 1 bps/Hz, α = 0.3, η = 0.9, dPDm = dPR = dSDm = dSR = dmn = dRDn = 1, θ = 2.

Table 1.

Figure 5.

Figure 6.

113

Simulation parameters.

DOI: http://dx.doi.org/10.5772/intechopen.89253

Notice that K<sup>ν</sup> is the modified Bessel function of the second kind and νth order [19].

Substituting Eqs. (27)–(32) into Eq. (20), we obtain the exact closed-form expression of outage probability for this RF-EH NOMA relaying system as follows:

$$P\_{out} = \begin{cases} I\_1 + I\_2 + I\_3 I\_4 [I\_5 + (1 - I\_5)I\_6], & \chi\_{th} < \frac{a\_n}{a\_m} - 1. \\\\ I\_1 + I\_3 I\_4 [I\_5 + (1 - I\_5)I\_6], & \frac{a\_n}{a\_m} - 1 < \chi\_{th} < \frac{a\_n}{a\_m} \\\\ \mathbf{1}, & \chi\_{th} > \frac{a\_n}{a\_m} .\end{cases} \tag{33}$$

#### 3.2 Throughput

At this point, we analyze throughput (Φ) at the destination node for delaylimited transmission mode. It is found out by evaluating outage probability at a fixed source transmission rate—Ω bps/Hz. We observe that the source transmit information at the rate of Ω bps/Hz and the effective communication time from the source to the destination in the block time T is (1-α)T/2. Therefore, throughput Φ at the destination is defined as follows:

$$\Phi = (\mathbf{1} - P\_{out})\Omega \frac{(\mathbf{1} - a)T/2}{T} = \frac{(\mathbf{1} - a)(\mathbf{1} - P\_{out})\Omega}{2}.\tag{34}$$

Substituting the result of Pout as Eq. (33) in Section 3.1 into Eq. (34), we obtain the exact closed-form expression of throughput for this RF-EH NOMA relaying system.

These derivations are similar to [20]. By using these expressions for programming, we can investigate the behaviors of this considered system, and then we can adjust the inputs to achieve the optimal performance for this network.

#### 4. Numerical results and discussion

In this section, we provide the numerical results according to the system key parameters (i.e., the average transmit SNR γ<sup>0</sup> and γS, number of users, time switching ratio, and power allocation coefficients) to clarify the performance of proposed protocol for this considered RF-EH NOMA relaying system. Furthermore, we also provide Monte Carlo simulation results to verify our analytical results. The simulation parameters are shown in Table 1.

Figure 5 depicts Pout of this considered system versus the average transmit power of power station with different numbers of users M. This figure shows that when we increase the transmit power of power station P, Pout of this system

Performance Analysis for NOMA Relaying System in Next-Generation Networks with RF Energy… DOI: http://dx.doi.org/10.5772/intechopen.89253


#### Table 1.

I<sup>6</sup> ¼ Pr Y<sup>3</sup> <

¼ FY<sup>3</sup>

Recent Wireless Power Transfer Technologies

¼ 1 � 2e

8 >>>>><

>>>>>:

Pout ¼

the destination is defined as follows:

4. Numerical results and discussion

simulation parameters are shown in Table 1.

<sup>Φ</sup> <sup>¼</sup> ð Þ <sup>1</sup> � Pout <sup>Ω</sup> ð Þ <sup>1</sup> � <sup>α</sup> <sup>T</sup>=<sup>2</sup>

order [19].

3.2 Throughput

system.

112

c3γth c2 � �

þ

r

∞ð

FY<sup>3</sup>

K1 2

Notice that K<sup>ν</sup> is the modified Bessel function of the second kind and νth

Substituting Eqs. (27)–(32) into Eq. (20), we obtain the exact closed-form expression of outage probability for this RF-EH NOMA relaying system as follows:

I<sup>1</sup> þ I<sup>2</sup> þ I3I4½ � I<sup>5</sup> þ ð Þ 1 � I<sup>5</sup> I<sup>6</sup> , γth <

1, γth>

At this point, we analyze throughput (Φ) at the destination node for delaylimited transmission mode. It is found out by evaluating outage probability at a fixed source transmission rate—Ω bps/Hz. We observe that the source transmit information at the rate of Ω bps/Hz and the effective communication time from the source to the destination in the block time T is (1-α)T/2. Therefore, throughput Φ at

Substituting the result of Pout as Eq. (33) in Section 3.1 into Eq. (34), we obtain the exact closed-form expression of throughput for this RF-EH NOMA relaying

These derivations are similar to [20]. By using these expressions for programming, we can investigate the behaviors of this considered system, and then we can

In this section, we provide the numerical results according to the system key

Figure 5 depicts Pout of this considered system versus the average transmit power of power station with different numbers of users M. This figure shows that when we increase the transmit power of power station P, Pout of this system

parameters (i.e., the average transmit SNR γ<sup>0</sup> and γS, number of users, time switching ratio, and power allocation coefficients) to clarify the performance of proposed protocol for this considered RF-EH NOMA relaying system. Furthermore, we also provide Monte Carlo simulation results to verify our analytical results. The

adjust the inputs to achieve the optimal performance for this network.

<sup>I</sup><sup>1</sup> <sup>þ</sup> <sup>I</sup>3I4½ � <sup>I</sup><sup>5</sup> <sup>þ</sup> ð Þ <sup>1</sup> � <sup>I</sup><sup>5</sup> <sup>I</sup><sup>6</sup> , an

c3γth c2

ffiffiffiffiffiffiffiffiffiffiffiffi γth λ2λ6c<sup>2</sup>

c3γth c2 � �

�c3γth <sup>λ</sup>2c<sup>2</sup>

<sup>þ</sup> Pr <sup>Y</sup><sup>3</sup> <sup>&</sup>lt; <sup>γ</sup>th

γth c2z � c3γth � �

ffiffiffiffiffiffiffiffiffiffiffiffi γth λ2λ6c<sup>2</sup> � � r

c2Y<sup>1</sup> � c3γth

:

am

<sup>T</sup> <sup>¼</sup> ð Þ <sup>1</sup> � <sup>α</sup> ð Þ <sup>1</sup> � Pout <sup>Ω</sup>

� �

f Y1 ð Þz dz

, Y1>

an am � 1:

an am :

<sup>2</sup> : (34)

an am :

� 1<γth <

c3γth c2

(32)

(33)

Simulation parameters.

#### Figure 5.

Pout vs. average transmit SNR of P with different numbers of users M with γ<sup>S</sup> = 20 dB, an = 0.9, m = 2, n = 3, Ω = 1 bps/Hz, α = 0.3, η = 0.9, dPDm = dPR = dSDm = dSR = dmn = dRDn = 1, θ = 2.

#### Figure 6.

Throughput Φ vs. average transmit SNR of P with different numbers of users M with γ<sup>S</sup> = 20 dB, an = 0.9, m = 2, n = 3, Ω = 1 bps/Hz, α = 0.3, η = 0.9, dPDm = dPR = dSDm = dSR = dmn = dRDn = 1, θ = 2.

decreases. Similarly, Figure 6 shows the variation of throughput with respect to γ<sup>0</sup> for different values of M. This figure also shows that the throughput of this system increases when increasing transmit power of power station P. These mean that we can improve the performance by increasing transmit power to provide more energy to users or reducing the NOMA of users.

greater than 1 � 2Ω/log2(an/am + 1), then Pout reaches 1. From this analysis, there exists a specific value of α<sup>∗</sup> that leads Pout to obtain the lowest value and leads Φ to reach the highest value. Obviously, we can select the best time switching ratio α to achieve the optimal performance of this system. From these figures, we also found that the performance of this system can be improved by increasing the transmit

Performance Analysis for NOMA Relaying System in Next-Generation Networks with RF Energy…

Figures 9 and 10 show the variation of Pout and throughput Φ with respect to power allocation coefficient an for different values of average transmit SNR of S, respectively. From these figures, we can see that when an ! 1, the performance of

to these figures, the performance can be improved when an ! 0.89 for Ω = 1 bps/Hz,

Pout with respect to power allocation coefficient an for different values of average transmit SNR of S with γ<sup>0</sup> = 20 dB, M = 8, m = 2, n = 3, Ω = 1 bps/Hz, α = 0.1, η = 0.9, dPDm = dPR = dSDm = dSR = dmn = dRDn = 1,

Throughput Φ with respect to power allocation coefficient for different values of average transmit SNR of S with γ<sup>0</sup> = 20 dB, M = 8, m = 2, n = 3, Ω = 1 bps/Hz, α = 0.1, η = 0.9, dPDm = dPR = dSDm = dSR = dmn = dRDn = 1,

�1 < an/am), by

�1. According

this system degrades. Due to the constrain of γth (i.e., γth = 22Ω/(1�α)

the given value of R and α, the Pout reaches 1 when an/am < 22Ω/(1�α)

power of source S.

DOI: http://dx.doi.org/10.5772/intechopen.89253

Figure 9.

Figure 10.

θ = 2.

115

θ = 2.

Figures 7 and 8 plot the curves of Pout and throughput Φ of this system versus time switching ratio for different values of average transmit power of S, respectively. From these figures, we found that when the time switching ratio α is small, α increases, then Pout decreases, and Φ increases. This can be explained by that there is more time for the user and relay to harvest energy as α grows. When α continues to increase, Pout inversely increases, and Φ decreases. The reason is that there is less time for message transmission phases when α is greater than α<sup>∗</sup> value. When α is

Figure 7.

Pout with respect to time switching ratio for different values of average transmit SNR of S with γ<sup>0</sup> = 20 dB, M = 8, m = 2, n = 3, Ω = 1 bps/Hz, an = 0.9, η = 0.9, dPDm = dPR = dSDm = dSR = dmn = dRDn = 1, θ = 2.

Figure 8.

Throughput Φ with respect to time switching ratio for different values of average transmit SNR of S with γ<sup>0</sup> = 20 dB, M = 8, m = 2, n = 3, Ω = 1 bps/Hz, an = 0.9, η = 0.9, dPDm = dPR = dSDm = dSR = dmn = dRDn = 1, θ = 2.

Performance Analysis for NOMA Relaying System in Next-Generation Networks with RF Energy… DOI: http://dx.doi.org/10.5772/intechopen.89253

greater than 1 � 2Ω/log2(an/am + 1), then Pout reaches 1. From this analysis, there exists a specific value of α<sup>∗</sup> that leads Pout to obtain the lowest value and leads Φ to reach the highest value. Obviously, we can select the best time switching ratio α to achieve the optimal performance of this system. From these figures, we also found that the performance of this system can be improved by increasing the transmit power of source S.

Figures 9 and 10 show the variation of Pout and throughput Φ with respect to power allocation coefficient an for different values of average transmit SNR of S, respectively. From these figures, we can see that when an ! 1, the performance of this system degrades. Due to the constrain of γth (i.e., γth = 22Ω/(1�α) �1 < an/am), by the given value of R and α, the Pout reaches 1 when an/am < 22Ω/(1�α) �1. According to these figures, the performance can be improved when an ! 0.89 for Ω = 1 bps/Hz,

#### Figure 9.

decreases. Similarly, Figure 6 shows the variation of throughput with respect to γ<sup>0</sup> for different values of M. This figure also shows that the throughput of this system increases when increasing transmit power of power station P. These mean that we can improve the performance by increasing transmit power to provide more energy

Figures 7 and 8 plot the curves of Pout and throughput Φ of this system versus time switching ratio for different values of average transmit power of S, respectively. From these figures, we found that when the time switching ratio α is small, α increases, then Pout decreases, and Φ increases. This can be explained by that there is more time for the user and relay to harvest energy as α grows. When α continues to increase, Pout inversely increases, and Φ decreases. The reason is that there is less time for message transmission phases when α is greater than α<sup>∗</sup> value. When α is

Pout with respect to time switching ratio for different values of average transmit SNR of S with γ<sup>0</sup> = 20 dB, M = 8, m = 2, n = 3, Ω = 1 bps/Hz, an = 0.9, η = 0.9, dPDm = dPR = dSDm = dSR = dmn = dRDn = 1, θ = 2.

Throughput Φ with respect to time switching ratio for different values of average transmit SNR of S with γ<sup>0</sup> = 20 dB, M = 8, m = 2, n = 3, Ω = 1 bps/Hz, an = 0.9, η = 0.9, dPDm = dPR = dSDm = dSR = dmn = dRDn = 1,

to users or reducing the NOMA of users.

Recent Wireless Power Transfer Technologies

Figure 7.

Figure 8.

θ = 2.

114

Pout with respect to power allocation coefficient an for different values of average transmit SNR of S with γ<sup>0</sup> = 20 dB, M = 8, m = 2, n = 3, Ω = 1 bps/Hz, α = 0.1, η = 0.9, dPDm = dPR = dSDm = dSR = dmn = dRDn = 1, θ = 2.

#### Figure 10.

Throughput Φ with respect to power allocation coefficient for different values of average transmit SNR of S with γ<sup>0</sup> = 20 dB, M = 8, m = 2, n = 3, Ω = 1 bps/Hz, α = 0.1, η = 0.9, dPDm = dPR = dSDm = dSR = dmn = dRDn = 1, θ = 2.

#### Figure 11.

Pout with and without relay vs. average transmit SNR of P with different numbers of users M with γ<sup>S</sup> = 20 dB, an = 0.9, m = 2, n = 3, Ω = 1 bps/Hz, α = 0.3, η = 0.9, dPDm = dPR = dSDm = dSR = dmn = dRDn = 1, θ = 2.

α = 0.1. In order to improve the performance of this system, we can allocate more transmit power for the worse user's message (i.e., sn). However, at that time the power which leaves for the better user's message (i.e., sm) will be smaller, and it should satisfy an/am > 22Ω/(1<sup>α</sup>) 1.

In addition, Figure 11 plots the curves of Pout with and without relay versus average transmit SNR of power station P with different numbers of users M. In this figure, we can observe that Pout of relaying scheme is lower than Pout without relaying. In other words, this result confirms that relaying method can improve the performance of this considered system.

Finally, we can observe from the above figures that the analysis and simulation results are good matching. This confirms the correctness of our analysis.

## 5. Conclusions

In this chapter, we have presented the performance analysis of downlink RF-EH NOMA relaying network with triple-phase harvest-transmit-forward transmission protocol in terms of outage probability and throughput. The exact closed-form expressions of outage probability and throughput for this proposed system have been derived. We have found that the performance of this considered system is enhanced by applying relaying technique or increasing the transmit power for energy harvesting and/or increasing the transmit power for information transmission. Moreover, the existence of best time switching ratio is proven to achieve the optimal performance of this system. We will solve the best time switching ratio searching problem in the future work.

Author details

\* and Jai P. Agrawal<sup>2</sup>

2 Purdue University Northwest, Hammond, IN, USA

\*Address all correspondence to: hadacbinh@duytan.edu.vn

© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

Performance Analysis for NOMA Relaying System in Next-Generation Networks with RF Energy…

DOI: http://dx.doi.org/10.5772/intechopen.89253

1 Duy Tan University, Da Nang, Vietnam

provided the original work is properly cited.

Dac-Binh Ha<sup>1</sup>

117

Performance Analysis for NOMA Relaying System in Next-Generation Networks with RF Energy… DOI: http://dx.doi.org/10.5772/intechopen.89253
