2. System and channel model description

Figure 3 depicts the system model for RF-EH NOMA relaying network, in which the power station (P) intends to transfer energy to energy-constrained relay (R) and energy-constrained destination nodes (D); information source (S) intends transmit the information to destinations by the help of relay node R.

Notation: Denote P, S, R, and D as power station, information source, relay, and destination, respectively. |hSDm| <sup>2</sup> and |hSDn| <sup>2</sup> are denoted as the ordered channel gains of the mth user and the nth user, respectively. Denote |hPR| 2 , |hPDm| 2 , |hSR| 2 , |hRDn| 2 , and |hmn| <sup>2</sup> as the channel gains of the links P—R, P—Dm, S—R, R—Dn, and Dm—Dn, respectively. Denote dPR, dPDm, dSR, dRDn, dSDm, and dmn as the Euclidean distances of P—R, P—Dm, S—R, S—Dm, R—Dn, and Dm—Dn, respectively. Symbol θ is denoted as the path loss exponent. Let X<sup>1</sup> = |hPDm| 2 , Y<sup>1</sup> = |hPR| 2 , X<sup>2</sup> = |hSDm| 2 , Y<sup>2</sup> = |hSR| 2 , X<sup>3</sup> = |hmn| 2 , and Y<sup>3</sup> = |hRDn| 2 .

In this system, NOMA scheme is applied for M destination users in pair division manner, such as {Dm, Dn} with m < n [17]. Without loss of generality, we assume that all the channel power gains between S and Di (1 ≤ i ≤ M) follow the following order: |hSD1| <sup>2</sup> ≥ … ≥ |hSDm| <sup>2</sup> ≥ |hSDn| <sup>2</sup> ≥ … ≥ |hSDM| 2 .

Figure 3. System model for RF-EH NOMA relaying network.

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


#### Figure 4.

• The exact closed-form expressions of outage probability and throughput for each link and whole system are derived by using the statistical characteristics of signal-to-noise ratio (SNR) and signal-to-interference-plus-noise ratio

• In terms of outage probability, the numerical results are provided according to the system key parameters, such as the transmit power, number of users, time

Figure 3 depicts the system model for RF-EH NOMA relaying network, in which the power station (P) intends to transfer energy to energy-constrained relay (R) and energy-constrained destination nodes (D); information source (S) intends

Notation: Denote P, S, R, and D as power station, information source, relay, and

Dm—Dn, respectively. Denote dPR, dPDm, dSR, dRDn, dSDm, and dmn as the Euclidean distances of P—R, P—Dm, S—R, S—Dm, R—Dn, and Dm—Dn, respectively. Symbol

In this system, NOMA scheme is applied for M destination users in pair division manner, such as {Dm, Dn} with m < n [17]. Without loss of generality, we assume that all the channel power gains between S and Di (1 ≤ i ≤ M) follow the following

<sup>2</sup> ≥ … ≥ |hSDM|

<sup>2</sup> as the channel gains of the links P—R, P—Dm, S—R, R—Dn, and

2 . 2

<sup>2</sup> are denoted as the ordered channel

, Y<sup>1</sup> = |hPR|

2 , |hPDm| 2 , |hSR| 2 ,

2

, X<sup>2</sup> = |hSDm|

2 ,

switching ratio, and power allocation coefficients to look insight this

transmit the information to destinations by the help of relay node R.

gains of the mth user and the nth user, respectively. Denote |hPR|

θ is denoted as the path loss exponent. Let X<sup>1</sup> = |hPDm|

, and Y<sup>3</sup> = |hRDn|

<sup>2</sup> ≥ |hSDn|

<sup>2</sup> and |hSDn|

2 .

(SINR) of transmission links.

Recent Wireless Power Transfer Technologies

2. System and channel model description

considered system.

destination, respectively. |hSDm|

, X<sup>3</sup> = |hmn|

2

<sup>2</sup> ≥ … ≥ |hSDm|

System model for RF-EH NOMA relaying network.

, and |hmn|

2


Y<sup>2</sup> = |hSR|

order: |hSD1|

Figure 3.

106

The triple-phase protocol for RF-EH NOMA relaying network.

The scenario of this considered system is investigated as follows:


In this work, we propose a triple-phase harvest-transmit-forward transmission protocol for this RF-EH NOMA relaying system as shown in Figure 4:


$$
\infty = \sqrt{a\_m}s\_m + \sqrt{a\_n}s\_n \tag{1}
$$

to user pair (Dm, Dn) in the time of (1�α)T/2, where sm and sn are the message for the mth user Dm and the nth user Dn, respectively, and am and an are the power allocation coefficients which satisfied the conditions: 0 < am < an and am + an = 1 by following the NOMA scheme. By applying NOMA, Dm uses SIC to detect message sn and subtracts this component from the received signal to obtain its own message sm.

3. In the third phase (information relaying phase): in this phase, Dm re-encodes and forwards sn to Dn in the remaining time of (1�α)T/2 with the energy harvested from P. At the same time, relay decodes x and forwards x to Dn.

Finally, Dn combines two received signals, that is, the relaying signals from Dm and R, to decode its own message by using selection combining (SC) scheme.

For more detailed purpose, we continue to present the transmission of this protocol for RF-EH NOMA relaying system in mathematical manner.

#### 2.1 Power transfer phase

In this phase, the energy of Dm and R harvested from P in the time of αT can be respectively expressed as

$$E\_1 = \frac{\eta P\_0 |h\_{PD\_m}|^2 \alpha T}{d\_{PD\_m}^{\theta}},\tag{2}$$

that we ignore the processing power required by the transmit/receive circuitry of Dm and R. Therefore, the transmit power of Dm and R is respectively given by

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

<sup>P</sup><sup>1</sup> <sup>¼</sup> <sup>2</sup>ηαP<sup>0</sup> hPDm j j<sup>2</sup> ð Þ <sup>1</sup> � <sup>α</sup> <sup>d</sup><sup>θ</sup>

<sup>P</sup><sup>2</sup> <sup>¼</sup> <sup>2</sup>ηαP0j j hPR

ffiffiffiffiffiffiffi P1 dθ mn s

am <sup>p</sup> sm <sup>þ</sup> ffiffiffiffiffi

Because Dn applies SC scheme, the instantaneous SNR/SINR at Dn to detect sn

, <sup>2</sup>ηαanγ<sup>0</sup> ð Þ <sup>1</sup> � <sup>α</sup> <sup>d</sup><sup>θ</sup>

PDm <sup>d</sup><sup>θ</sup> mn

Xm�1 k¼0

M! ð Þ M � m !ð Þ m � 1 !

The independent and identically distributed (IID) Rayleigh channel gains (X1, Y1, X2, Y2, X3, Y3) follow exponential distributions with parameters λ1, λ2, λ3, λ4, λ5, and λ6, respectively. According to [18], the cumulative distribution function (CDF) and the probability density function (PDF) of ordered random variable X<sup>2</sup> are

> Cm�<sup>1</sup> <sup>k</sup> ð Þ �<sup>1</sup> <sup>k</sup> M � m þ k þ 1

> > 1 λ3 Xm�1 k¼0

Because all links undergo Rayleigh fading, the PDF and CDF of random variable

1 λ e �x

f <sup>V</sup>ð Þ¼ x

C<sup>m</sup>�<sup>1</sup> <sup>k</sup> ð Þ �<sup>1</sup> <sup>k</sup>

yDmDn ¼

ffiffiffiffiffiffiffiffiffi P2 dθ RDn <sup>s</sup> ffiffiffiffiffiffi

j j hmn <sup>2</sup>

PDm <sup>d</sup><sup>θ</sup> mn

� �,

<sup>σ</sup><sup>2</sup> ,c<sup>1</sup> <sup>¼</sup> <sup>2</sup>ηαγ<sup>0</sup> ð Þ <sup>1</sup> � <sup>α</sup> <sup>d</sup><sup>θ</sup>

M! ð Þ M � m !ð Þ m � 1 !

V ∈{X1, Y1, Y2, X3, Y3} have the following forms:

ð Þ c3Y<sup>3</sup> þ 1

), and

).

<sup>2</sup>ηαγ<sup>0</sup> hPDm j j<sup>2</sup>

ð Þ <sup>1</sup> � <sup>α</sup> <sup>d</sup><sup>θ</sup>

<sup>¼</sup> max <sup>c</sup>1X1X3, <sup>c</sup>2Y1Y<sup>3</sup>

yRDn ¼

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

expressed as

γ sn Dn ¼ max

where nmn� CN(0,σ<sup>2</sup>

where nRDn� CN(0,σ<sup>2</sup>

where <sup>γ</sup><sup>0</sup> <sup>¼</sup> <sup>P</sup><sup>0</sup>

respectively written as follows

f X2 ð Þ¼ x

FX<sup>2</sup> ð Þ¼ x

109

transmitted from S can be given by

8 < : ð Þ <sup>1</sup> � <sup>α</sup> <sup>d</sup><sup>θ</sup>

The received signals at Dn that are transmitted from Dm and R are, respectively,

PDm

PR

an

PR

2

, (9)

: (10)

snhmn þ nmn, (11)

<sup>p</sup> ð Þ sn hRDn <sup>þ</sup> nRDn , (12)

j j hPR

, <sup>c</sup><sup>2</sup> <sup>¼</sup> <sup>2</sup>ηαanγ<sup>0</sup> ð Þ <sup>1</sup> � <sup>α</sup> <sup>d</sup><sup>θ</sup>

amγ<sup>0</sup> hRDn j j<sup>2</sup> <sup>þ</sup> <sup>d</sup><sup>θ</sup>

� �

PRd<sup>θ</sup> RDn

1 � e

e

�x Mð Þ �mþkþ1 λ3 h i, (14)

�x Mð Þ �mþkþ1

<sup>λ</sup> , (16)

<sup>λ</sup><sup>3</sup> : (15)

<sup>2</sup> hRDn j j<sup>2</sup>

RDn

9 = ;

,c<sup>3</sup> <sup>¼</sup> amγ<sup>0</sup> dθ RDn : (13)

$$E\_2 = \frac{\eta P\_0 |h\_{PR}|^2 aT}{d\_{PR}^{\theta}},\tag{3}$$

where η is the energy conversion efficiency (0 ≤ η ≤ 1).

#### 2.2 Information transmitting phase

In this duration of (1�α)T/2, the source S broadcasts superimposed message signal x as Eq. (1) to the user pair and relay. The received signal at Dm is written as

$$\mathcal{Y}\_{\text{SD}\_m} = \sqrt{\frac{P\_{\text{S}}}{d\_{\text{SD}\_m}^{\theta}}} (\sqrt{a\_m}s\_m + \sqrt{a\_n}s\_n)h\_{\text{SD}\_m} + n\_{\text{SD}\_m},\tag{4}$$

where nSDm � CN(0,σ<sup>2</sup> ) is AWGN. Similarly, the received signal at R is expressed as

$$\mathcal{y}\_{\text{SR}} = \sqrt{\frac{P\_{\text{S}}}{d\_{\text{SR}}^{\theta}}} (\sqrt{a\_m}\mathfrak{s}\_m + \sqrt{a\_n}\mathfrak{s}\_n)h\_{\text{SR}} + \mathfrak{n}\_{\text{SR}},\tag{5}$$

where nSR � CN(0,σ<sup>2</sup> ) are AWGN.

Applying NOMA, Dm uses SIC to detect message sn and subtracts this component from the received signal to obtain its own message sm. Therefore, the instantaneous SINR at Dm to detect sm and sn transmitted from S can be respectively given by

$$\gamma\_{\text{SD}\_m}^{\prime\_n} = \frac{a\_n \chi\_S |h\_{\text{SD}\_m}|^2}{a\_m \chi\_S |h\_{\text{SD}\_m}|^2 + d\_{\text{SD}\_m}^{\theta}} = \frac{b\_2 X\_2}{b\_1 X\_2 + \mathbf{1}},\tag{6}$$

$$\left|\gamma\_{SD\_m}^{\prime\_m} = \frac{a\_m \gamma\_S \left|h\_{SD\_m}\right|^2}{d\_{SD\_m}^{\theta}} = b\_1 X\_2,\tag{7}$$

$$\text{where } \gamma\_S = \frac{P\_S}{\sigma^2}, b\_1 = \frac{a\_m \gamma\_S}{d\_{SD\_m}^{\vartheta}}, \ b\_2 = \frac{a\_n \gamma\_S}{d\_{SD\_m}^{\vartheta}}.$$

And in the meanwhile the relay applying DF scheme first decodes its received signal from S to obtain superimposed message x and then re-encodes and forwards it to the destination. Therefore, in this phase the instantaneous SNR at R to detect x transmitted from S can be given by

$$\chi\_{\rm SR}^{\rm x} = \frac{\chi\_{\rm S}|h\_{\rm SR}|^2}{d\_{\rm SR}^{\theta}} = b\_{\rm 3} Y\_2,\tag{8}$$
 
$$\text{where } b\_{\rm 3} = \frac{\chi\_{\rm S}}{d\_{\rm SR}^{\theta}}.$$

#### 2.3 Information relaying phase

In this phase, Dm and R spend the harvested energy E<sup>1</sup> and E2, respectively, as Eqs. (2) and (3) to forward received signals to Dn in duration of (1�α)T/2. Notice Performance Analysis for NOMA Relaying System in Next-Generation Networks with RF Energy… DOI: http://dx.doi.org/10.5772/intechopen.89253

that we ignore the processing power required by the transmit/receive circuitry of Dm and R. Therefore, the transmit power of Dm and R is respectively given by

$$P\_1 = \frac{2\eta\alpha P\_0|h\_{PD\_m}|^2}{(1-\alpha)d\_{PD\_m}^{\theta}},\tag{9}$$

$$P\_2 = \frac{2\eta a P\_0 \left| h\_{PR} \right|^2}{(1 - a)d\_{PR}^{\theta}}. \tag{10}$$

The received signals at Dn that are transmitted from Dm and R are, respectively, expressed as

$$\mathcal{Y}\_{D\_m D\_n} = \sqrt{\frac{P\_1}{d\_{mn}^{\theta}}} s\_n h\_{mn} + n\_{mn},\tag{11}$$

where nmn� CN(0,σ<sup>2</sup> ), and

<sup>E</sup><sup>1</sup> <sup>¼</sup> <sup>η</sup>P<sup>0</sup> hPDm j j<sup>2</sup>

<sup>E</sup><sup>2</sup> <sup>¼</sup> <sup>η</sup>P0j j hPR

where η is the energy conversion efficiency (0 ≤ η ≤ 1).

ffiffiffiffiffiffiffiffiffi PS dθ SDm <sup>s</sup> ffiffiffiffiffiffi

) is AWGN.

ffiffiffiffiffiffiffi PS dθ SR <sup>s</sup> ffiffiffiffiffiffi am <sup>p</sup> sm <sup>þ</sup> ffiffiffiffiffi

) are AWGN.

SDm <sup>¼</sup> anγ<sup>S</sup> hSDm j j<sup>2</sup>

γ sm

where <sup>γ</sup><sup>S</sup> <sup>¼</sup> PS

γx

SR <sup>¼</sup> <sup>γ</sup>Sj j hSR

dθ SR

where <sup>b</sup><sup>3</sup> <sup>¼</sup> <sup>γ</sup><sup>S</sup>

In this phase, Dm and R spend the harvested energy E<sup>1</sup> and E2, respectively, as Eqs. (2) and (3) to forward received signals to Dn in duration of (1�α)T/2. Notice

amγ<sup>S</sup> hSDm j j<sup>2</sup> <sup>þ</sup> <sup>d</sup><sup>θ</sup>

SDm <sup>¼</sup> amγ<sup>S</sup> hSDm j j<sup>2</sup> dθ SDm

> <sup>σ</sup><sup>2</sup> , <sup>b</sup><sup>1</sup> <sup>¼</sup> amγ<sup>S</sup> dθ SDm

And in the meanwhile the relay applying DF scheme first decodes its received signal from S to obtain superimposed message x and then re-encodes and forwards it to the destination. Therefore, in this phase the instantaneous SNR at R to detect

2

dθ SR :

Similarly, the received signal at R is expressed as

ySR ¼

γ sn

x transmitted from S can be given by

2.3 Information relaying phase

108

2.2 Information transmitting phase

Recent Wireless Power Transfer Technologies

where nSDm � CN(0,σ<sup>2</sup>

where nSR � CN(0,σ<sup>2</sup>

ySDm ¼

dθ PDm

> dθ PR

In this duration of (1�α)T/2, the source S broadcasts superimposed message signal x as Eq. (1) to the user pair and relay. The received signal at Dm is written as

> am <sup>p</sup> sm <sup>þ</sup> ffiffiffiffiffi

αT

2 αT

an

an

SDm

<sup>¼</sup> <sup>b</sup>2X<sup>2</sup> b1X<sup>2</sup> þ 1

, <sup>b</sup><sup>2</sup> <sup>¼</sup> anγ<sup>S</sup> dθ SDm :

, (6)

¼ b1X2, (7)

¼ b3Y2, (8)

Applying NOMA, Dm uses SIC to detect message sn and subtracts this component from the received signal to obtain its own message sm. Therefore, the instantaneous SINR at Dm to detect sm and sn transmitted from S can be respectively given by

<sup>p</sup> ð Þ sn hSDm <sup>þ</sup> nSDm , (4)

<sup>p</sup> ð Þ sn hSR <sup>þ</sup> nSR, (5)

, (2)

, (3)

$$\mathcal{Y}\_{\text{RD}\_{\pi}} = \sqrt{\frac{P\_2}{d\_{\text{RD}\_{\pi}}^{\theta}}} (\sqrt{a\_m}s\_m + \sqrt{a\_n}s\_n)h\_{\text{RD}\_{\pi}} + n\_{\text{RD}\_{\pi}},\tag{12}$$

where nRDn� CN(0,σ<sup>2</sup> ).

Because Dn applies SC scheme, the instantaneous SNR/SINR at Dn to detect sn transmitted from S can be given by

$$\begin{split} \gamma\_{D\_{n}}^{\kappa} &= \max \left\{ \frac{2\eta\alpha\gamma\_{0}|h\_{PD\_{n}}|^{2}|h\_{mn}|^{2}}{(1-\alpha)d\_{PD\_{n}}^{\theta}d\_{mn}^{\theta}}, \frac{2\eta\alpha a\_{n}\gamma\_{0}}{(1-\alpha)d\_{PR}^{\theta}} \frac{|h\_{PR}|^{2}|h\_{RD\_{n}}|^{2}}{\left(a\_{m}\gamma\_{0}|h\_{RD\_{n}}|^{2} + d\_{RD\_{n}}^{\theta}\right)} \right\} \\ &= \max \left\{ c\_{1}X\_{1}X\_{3}, \frac{c\_{2}Y\_{1}Y\_{3}}{(c\_{3}Y\_{3}+1)} \right\}, \\ \text{where } \gamma\_{0} &= \frac{P\_{0}}{\sigma^{2}}, c\_{1} = \frac{2\eta\alpha\gamma\_{0}}{(1-\alpha)d\_{PD\_{n}}^{\theta}d\_{mn}^{\theta}}, \ c\_{2} = \frac{2\eta\alpha a\_{n}\gamma\_{0}}{(1-\alpha)d\_{PR}^{\theta}d\_{RD\_{n}}^{\theta}}, c\_{3} = \frac{a\_{m}\gamma\_{0}}{d\_{RD\_{n}}^{\theta}}. \end{split} \tag{13}$$

The independent and identically distributed (IID) Rayleigh channel gains (X1, Y1, X2, Y2, X3, Y3) follow exponential distributions with parameters λ1, λ2, λ3, λ4, λ5, and λ6, respectively. According to [18], the cumulative distribution function (CDF) and the probability density function (PDF) of ordered random variable X<sup>2</sup> are respectively written as follows

$$F\_{X\_2}(\mathbf{x}) = \frac{M!}{(M-m)!(m-1)!} \sum\_{k=0}^{m-1} \frac{C\_k^{m-1}(-\mathbf{1})^k}{M-m+k+1} \left[ \mathbf{1} - e^{\frac{-x(M-m+k+1)}{\lambda\_3}} \right],\tag{14}$$

$$f\_{X\_2}(\mathbf{x}) = \frac{M!}{(M-m)!(m-1)!} \frac{1}{\lambda\_3} \sum\_{k=0}^{m-1} C\_k^{m-1} (-1)^k e^{\frac{-x(M-m+k+1)}{\lambda\_3}}.\tag{15}$$

Because all links undergo Rayleigh fading, the PDF and CDF of random variable V ∈{X1, Y1, Y2, X3, Y3} have the following forms:

$$f\_V(\mathbf{x}) = \frac{1}{\lambda} e^{-\frac{\mathbf{x}}{\lambda}},\tag{16}$$

$$F\_V(x) = \mathbf{1} - e^{-\frac{x}{\lambda}},\tag{17}$$

<sup>I</sup><sup>6</sup> <sup>¼</sup> Pr <sup>c</sup>2Y1Y<sup>3</sup>

an am

> an am

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, γth>

<sup>b</sup><sup>2</sup> � <sup>b</sup>1γth � �, <sup>γ</sup>th <sup>&</sup>lt;

1 � e

e

am

0, γth>

ð Þz dz ¼

� <sup>γ</sup>th

0, γth>

�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 � 1

an am � 1

> an am � 1

> > an am

�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;

�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 � �, an

am

λ1 e � z <sup>λ</sup>1dz

<sup>λ</sup>4b<sup>3</sup> : (31)

an am

� 1<γth <

1 � e

1 � e

∞ð

1 � e � <sup>γ</sup>th λ5c1z � � 1

0

�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

I2, I3, I4, I5, and I6, respectively, as follows:

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

1, γth>

<sup>b</sup><sup>2</sup> � <sup>b</sup>1γth � �, <sup>γ</sup>th <sup>&</sup>lt;

Xm�1 k¼0

γth

0, γth>

C<sup>m</sup>�<sup>1</sup> <sup>k</sup> ð Þ �<sup>1</sup> <sup>k</sup> M � m þ k þ 1

� �, <sup>γ</sup>th <sup>&</sup>lt;

<sup>b</sup><sup>2</sup> � <sup>b</sup>1γth � �, an

0, γth>

Xm�1 k¼0

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

C<sup>m</sup>�<sup>1</sup> <sup>k</sup> ð Þ �<sup>1</sup> <sup>k</sup> M � m þ k þ 1

γth c1z � �<sup>f</sup> <sup>X</sup><sup>1</sup>

:

I<sup>5</sup> ¼ 1 � e

Xm�1 k¼0

γth

M! ð Þ M � m !ð Þ m � 1 !

� FX<sup>2</sup>

γth b1

γth

ð Þ M � m !ð Þ m � 1 !

ð Þ M � m !ð Þ m � 1 !

c1X<sup>1</sup> � �

> ffiffiffiffiffiffiffiffiffiffiffiffi γth λ1λ5c<sup>1</sup>

¼ ∞ð

K1 2

0 FX<sup>3</sup>

ffiffiffiffiffiffiffiffiffiffiffiffi γth λ1λ5c<sup>1</sup> � � r

I<sup>1</sup> ¼

¼

I<sup>2</sup> ¼

¼

I<sup>3</sup> ¼

¼

111

FX<sup>2</sup>

8 >>><

>>>:

8 >>><

>>>:

8 >>><

>>>:

8 >>><

>>>:

8

>>>>>>>><

>>>>>>>>:

8

>>>>>>>>>><

>>>>>>>>>>:

FX<sup>2</sup>

γth b1 � �

M! ð Þ M � m !ð Þ m � 1 !

1 � FX<sup>2</sup>

<sup>1</sup> � <sup>M</sup>!

<sup>1</sup> � <sup>M</sup>!

<sup>I</sup><sup>4</sup> <sup>¼</sup> Pr <sup>X</sup><sup>3</sup> <sup>&</sup>lt; <sup>γ</sup>th

r

¼ 1 � 2

1 � FX<sup>2</sup>

By the help of Eqs. (14)–(17), we obtain the exact closed-form expressions of I1,

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

<sup>c</sup>3Y<sup>3</sup> <sup>þ</sup> <sup>1</sup> <sup>&</sup>lt; <sup>γ</sup>th � �: (26)

an am :

�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 : (27)

an am � 1:

(28)

an am � 1:

> an am :

� 1<γth <

an am :

(29)

(30)

an am � 1:

where λ ∈ {λ1, λ2, λ4, λ5, λ6}.
