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Outage probability for a multiuser NOMA-based network using energy harvesting relays

  • Rifqah Press and Vipin Balyan EMAIL logo
Published/Copyright: December 21, 2022
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Nonlinear Engineering
From the journal Nonlinear Engineering Volume 11 Issue 1

Abstract

This article evaluates the energy-harvesting capabilities of a multiuser non-orthogonal multiple access-based system, where energy harvesting relays utilise the power splitting relaying protocol to harvest energy and amplify-and-forward protocol to forward the signals to the connected users. The expressions for each user’s energy harvesting outage probability are calculated and compared to the same system model without energy harvesting. Simulation results show the effectiveness of the energy-harvesting relay nodes and the improved outage probability of each user.

Keywords: NOMA; energy harvesting; power splitting protocol; amplify-and-forward; outage probability

1 Introduction

Energy harvesting in wireless communication networks has garnered much attention recently; it is a proposed solution to self-sustaining and lifetime extension of wireless networks. It is argued that battery replacement and charging can be done; however, it can be costly and inconvenient, especially if the location of the batteries is not ideal. There are environmental energy-harvesting techniques such as wind, solar, and vibration; however, radio frequency (RF) wireless energy transfer is a more controlled, convenient, and safer way to harvest energy from the environment. RF signals contain information and energy; thus, an energy-harvesting node can simultaneously harvest and process information. A relay in a cooperative wireless network needs to have sufficient energy to stay active; therefore, a relay node with energy-harvesting capabilities is an excellent advantage in a wireless network [1,2].

Research in cooperative networks shows the benefits of energy-harvesting nodes, such as an increase in the life span of the nodes and the self-sustainability of a communication network, especially for 5G applications. The energy-harvesting employs different receiver architectures, power splitting, and time switching, thus enabling two protocols: power splitting relaying (PSR) and time switching relaying (TSR). The authors of refs [3,4,5,6] utilise the most widely used PSR protocol, whereas ref. [7] utilises the TSR protocol. However, refs [8] and [2] utilise both protocols and evaluate the performance of each. Moreover, ref. [8] reports the superiority of the PSR protocol, whereas ref. [2] reports that the latter is superior. Many researchers only implement one energy-harvesting scheme into their system model; however, refs [3] and [9] implement three different relay schemes. To explore the comparison of the proposed schemes, [3] implements adaptable PSR schemes, whereas [9] increases the security of the communication system. The previous studies [9,10] focus on the physical layer security of the communication system, where the base station transmits a jamming signal to mitigate interference from the eavesdropper node.

2 System model

The system model is similar to that shown in ref. [11]; however, the two relays employ energy-harvesting capabilities. This article follows the layout and the method presented in ref. [11]: the system model in which user connections, time subslots, power allocation, decoding order, and outage probability conditions are the same, thus avoiding repetition.

2.1 Time sub-slot t s 1

The active users in the network are UE 1 , UE 2 , UE 3 , and UE 4 . The status of these users in t s 1 is according to their locations, as shown in Figure 1: UE 1 and UE 2 are cell centre users connected directly to the base station and UE 3 and UE 4 are cell edge users connected to relay r 2 and r 1 , respectively. The base station transmits the superimposed signal to the connected UEs given by Eq. (1) from [11]:

(1) x s ( t s 1 ) = P 1 t s 1 P s x 1 ( t s 1 ) + P 2 t s 1 P s x 2 ( t s 1 ) + P 3 t s 1 P s x 3 ( t s 1 ) + P 4 t s 1 P s x 4 ( t s 1 ) .

Figure 1 System model 1.
Figure 1

System model 1.

The received signals at UE 1 , UE 2 , r 1 , and r 2 are given by Eq. (2) from [11]:

(2) y 1 ( t s 1 ) = h 1 BS x s ( t s 1 ) + N 1 ,

(3) y 2 ( t s 1 ) = h 2 BS x s ( t s 1 ) + N 2 ,

(4) y r 1 ( t s 1 ) = h r 1 BS x s ( t s 1 ) + N r 1 ,

(5) y r 2 ( t s 1 ) = h r 2 BS x s ( t s 1 ) + N r 2 .

The decoding order follows that of ref. [11], for time sub-slot t s 1 . The decoded SINRs at UE 1 are given by Eq. (3) from refs. [11,12], with the decoded SINR of UE 1 given by Eq. (4) from ref. [11]:

(6) SINR t s 1 4 − 1 = P 4 t s 1 P s ∣ h 1 BS ∣ 2 ∑ j = 1 3 P j t s 1 P s ∣ h 1 BS ∣ 2 + σ 1 2 ,

(7) SINR t s 1 3 − 1 = P 3 t s 1 P s ∣ h 1 BS ∣ 2 ∑ j = 1 2 P j t s 1 P s ∣ h 1 BS ∣ 2 + σ 1 2 ,

(8) SINR t s 1 2 − 1 = P 2 t s 1 P s ∣ h 1 BS ∣ 2 P 1 t s 1 P s ∣ h 1 BS ∣ 2 + σ 1 2 ,

(9) SINR t s 1 1 − 1 = P 1 t s 1 P s ∣ h 1 BS ∣ 2 σ 1 2 .

The decoded SINRs at UE 2 are given by Eq. (7) from [11], with the decoded SINR of UE 2 given by Eq. (8) from [11]

(10) SINR t s 1 4 − 2 = P 4 t s 1 P s ∣ h 2 BS ∣ 2 ∑ j = 1 3 P j t s 1 P s ∣ h 2 BS ∣ 2 + σ 2 2 ,

(11) SINR t s 1 3 − 2 = P 3 t s 1 P s ∣ h 2 BS ∣ 2 ∑ j = 1 2 P j t s 1 P s ∣ h 2 BS ∣ 2 + σ 2 2 ,

(12) SINR t s 1 2 − 2 = P 2 t s 1 P s ∣ h 2 BS ∣ 2 P 1 t s 1 P s ∣ h 2 BS ∣ 2 + σ 2 2 .

The energy-harvesting does not affect UE 1 and UE 2 as it is not connected to a relay. The PSR splits the received superimposed signal by a portion ρ y r i ( t s 1 ) utilised by the energy-harvesting receiver, given by Eq. (13), for i = 1 , 2 .

(13) ρ y r i ( t s 1 ) = ρ P 1 t s 1 P s x 1 ( t s 1 ) h r i BS + ρ P 2 t s 1 P s x 2 ( t s 1 ) h r i BS + ρ P 3 t s 1 P s x 3 ( t s 1 ) h r i BS + ρ P 4 t s 1 P s x 4 ( t s 1 ) h r i BS + ρ N r i .

With the remaining power of the received signal ( 1 − ρ ) y r i ( t s 1 ) utilised by the information receiver, given by

(14) ( 1 − ρ ) y r i ( t s 1 ) = ( 1 − ρ ) P 1 t s 1 P s x 1 ( t s 1 ) h r i BS + ( 1 − ρ ) P 2 t s 1 P s x 2 ( t s 1 ) h r i BS + ( 1 − ρ ) P 3 t s 1 P s x 3 ( t s 1 ) h r i BS + ( 1 − ρ ) P 4 t s 1 P s x 4 ( t s 1 ) h r i BS + ( 1 − ρ ) N r i .

The decoded SINR at relays r 1 and r 2 are given by

(15) SINR t s 1 4 − r 1 = ( 1 − ρ ) P 4 t s 1 P s ∣ h r 1 BS ∣ 2 ∑ j = 1 3 ( 1 − ρ ) P j t s 1 P s ∣ h r 1 BS ∣ 2 + ( 1 − ρ ) σ r 1 2 ,

(16) SINR t s 1 4 − r 2 = ( 1 − ρ ) P 4 t s 1 P s ∣ h r 2 BS ∣ 2 ∑ j = 1 3 ( 1 − ρ ) P j t s 1 P s ∣ h r 2 BS ∣ 2 + ( 1 − ρ ) σ r 2 2 ,

(17) SINR t s 1 3 − r 2 = ( 1 − ρ ) P 3 t s 1 P s ∣ h r 2 BS ∣ 2 ∑ j = 1 2 ( 1 − ρ ) P j t s 1 P s ∣ h r 2 BS ∣ 2 + ( 1 − ρ ) σ r 2 2 .

In the first block-time, the energy-harvesting receiver at r 1 and r 2 harvests the energy from the received signal given by Eq. (18), for i = 1 , 2 . The energy conversion efficiency is η with values between 0 < η < 1 .

(18) EH r i = η ρ P s ∣ h r i BS ∣ 2 ( P 1 t s 1 + P 2 t s 1 + P 3 t s 1 + P 4 t s 1 ) T / 2 = η ρ P s ∣ h r i BS ∣ 2 T / 2 .

The harvested energy is used to power the relays; thus, the relay power is given by

(19) P r i = EH r i T / 2 = η ρ P s ∣ h r i BS ∣ 2 .

2.2 Time sub-slot t s 2

In the second block-time, the amplify-and-forward (AF) protocol utilises an amplifying factor G r i given by

(20) G r i = 1 ( 1 − ρ ) P s ∣ h r i BS ∣ 2 ( P 1 t s 1 + P 2 t s 1 + P 3 t s 1 + P 4 t s 1 ) + σ R i 2 = 1 ( 1 − ρ ) P s ∣ h r i BS ∣ 2 + σ R i 2 .

The relays regenerate the signals for the users connected to it with the amplification given by Eqs. (21) and (22).

(21) x s r 1 ( t s 2 ) = ( 1 − ρ ) P 4 t s 2 G r 1 P s P r 1 x 4 ( t s 1 ) h r 1 BS ,

(22) x s r 2 ( t s 2 ) = ( 1 − ρ ) P 3 t s 2 G r 2 P s P r 2 x 3 ( t s 1 ) h r 2 BS .

The received signals of UE 3 and UE 4 are given by Eqs. (23) and (24).

(23) y 3 ( t s 2 ) = h 3 r 2 x s r 2 ( t s 2 ) + N 3 ,

(24) y 4 ( t s 2 ) = h 4 r 1 x s r 1 ( t s 2 ) + N 4 .

Combining Eqs. (19)–(24), the decoded SINRs at UE 3 and UE 4 are given by

(25) SINR t s 2 3 − 3 = ( 1 − ρ ) η ρ P 3 t s 2 P s 2 ( ∣ h r 2 BS ∣ 2 ) 2 ∣ h 3 r 2 ∣ 2 ( 1 − ρ ) P s ∣ h r 2 BS ∣ 2 σ 3 2 + σ R 2 2 σ 3 2 ,

(26) SINR t s 2 4 − 4 = ( 1 − ρ ) η ρ P 4 t s 2 P s 2 ( ∣ h r 1 BS ∣ 2 ) 2 ∣ h 4 r 1 ∣ 2 ( 1 − ρ ) P s ∣ h r 1 BS ∣ 2 σ 4 2 + σ R 1 2 σ 4 2 .

2.3 Time sub-slot t s 3

In this time sub-slot, the UEs status changes according to their new locations as shown in Figure 2, with the following connections: UE 1 is a cell centre user connected directly to the base station and UE 2 , UE 3 , and UE 4 are cell edge users with UE 3 connected to r 1 , and UE 2 and UE 4 connected to r 2 . The base station transmits the superimposed signal to the connected UEs given by

(27) x s ( t s 3 ) = P 1 t s 3 P s x 1 ( t s 3 ) + P 2 t s 3 P s x 2 ( t s 3 ) + P 3 t s 3 P s x 3 ( t s 3 ) + P 4 t s 3 P s x 4 ( t s 3 ) .

Figure 2 System model 2.
Figure 2

System model 2.

The received signals at UE 1 , r 1 , and r 2 are given by Eqs. (28)–(30).

(28) y 1 ( t s 3 ) = h 1 BS x s ( t s 3 ) + N 1 ,

(29) y r 1 ( t s 3 ) = h r 1 BS x s ( t s 3 ) + N r 1 ,

(30) y r 2 ( t s 3 ) = h r 2 BS x s ( t s 3 ) + N r 2 .

The decoded SINRs at UE 1 are given by Eqs. (31)–(34)

(31) SINR t s 3 3 − 1 = P 3 t s 3 P s ∣ h 1 BS ∣ 2 ∑ j = 1 2 P j t s 3 P s ∣ h 1 BS ∣ 2 + P 4 t s 3 P s ∣ h 1 BS ∣ 2 + σ 1 2 ,

(32) SINR t s 3 4 − 1 = P 4 t s 3 P s ∣ h 1 BS ∣ 2 ∑ j = 1 2 P j t s 3 P s ∣ h 1 B S ∣ 2 + σ 1 2 ,

(33) SINR t s 3 2 − 1 = P 2 t s 3 P s ∣ h 1 BS ∣ 2 P 1 t s 3 P s ∣ h 1 BS ∣ 2 + σ 1 2 ,

(34) SINR t s 3 1 − 1 = P 1 t s 3 P s ∣ h 1 BS ∣ 2 σ 1 2 .

As previously stated in Section 2.1, the PSR protocol splits the received signal by ρ : ( 1 − ρ ) , resulting in Eqs. (35) and (36), for i = 1 , 2 .

(35) ρ y r i ( t s 3 ) = ρ P 1 t s 3 P s x 1 ( t s 3 ) h r i BS + ρ P 2 t s 3 P s x 2 ( t s 3 ) h r i BS + ρ P 3 t s 3 P s x 3 ( t s 3 ) h r i BS + ρ P 4 t s 3 P s x 4 ( t s 3 ) h r i BS + ρ N r i ,

(36) ( 1 − ρ ) y r i ( t s 3 ) = ( 1 − ρ ) P 1 t s 3 P s x 1 ( t s 3 ) h r i BS + ( 1 − ρ ) P 2 t s 3 P s x 2 ( t s 3 ) h r i BS + ( 1 − ρ ) P 3 t s 3 P s x 3 ( t s 3 ) h r i BS + ( 1 − ρ ) P 4 t s 3 P s x 4 ( t s 3 ) h r i BS + ( 1 − ρ ) N r i .

Eqs. (37)–(40) give the decoded SINR at the relays in time sub-slot t s 3 .

(37) SINR t s 3 3 − r 1 = ( 1 − ρ ) P 3 t s 3 P s ∣ h r 1 BS ∣ 2 ∑ j = 1 2 ( 1 − ρ ) P j t s 3 P s ∣ h r 1 BS ∣ 2 + ( 1 − ρ ) P 4 t s 3 P s ∣ h r 1 BS ∣ 2 + ( 1 − ρ ) σ r 1 2 ,

(38) SINR t s 3 3 − r 2 = ( 1 − ρ ) P 3 t s 3 P s ∣ h r 2 BS ∣ 2 ∑ j = 1 2 ( 1 − ρ ) P j t s 3 P s ∣ h r 2 BS ∣ 2 + ( 1 − ρ ) P 4 t s 3 P s ∣ h r 2 BS ∣ 2 + ( 1 − ρ ) σ r 2 2 ,

(39) SINR t s 3 4 − r 2 = ( 1 − ρ ) P 4 t s 3 P s ∣ h r 2 BS ∣ 2 ∑ j = 1 2 ( 1 − ρ ) P j t s 3 P s ∣ h r 2 BS ∣ 2 + ( 1 − ρ ) σ r 2 2 ,

(40) SINR t s 3 2 − r 2 = ( 1 − ρ ) P 2 t s 3 P s ∣ h r 2 B S ∣ 2 ( 1 − ρ ) P 1 t s 3 P s ∣ h r 2 BS ∣ 2 + ( 1 − ρ ) σ r 2 2 .

The energy-harvesting equations in Section 2.1 are not time dependent; thus, they are utilised in this time sub-slot as well.

2.4 Time sub-slot t s 4

The relays regenerate the signals for the users connected to it, given by the following equations:

(41) x s r 1 ( t s 4 ) = ( 1 − ρ ) P 3 t s 4 G r 1 P s P r 1 x 3 ( t s 3 ) h r 1 BS ,

(42) x s r 2 ( t s 4 ) = ( 1 − ρ ) P 2 t s 4 G r 2 P s P r 2 x 2 ( t s 3 ) h r 2 BS + ( 1 − ρ ) P 4 t s 4 G r 2 P s P r 2 x 4 ( t s 3 ) h r 2 BS .

The received signals of UE 2 , UE 3 , and UE 4 are given by Eqs. (43)–(45).

(43) y 2 ( t s 4 ) = h 2 r 2 x s r 2 ( t s 4 ) + N 2 ,

(44) y 3 ( t s 4 ) = h 3 r 1 x s r 1 ( t s 4 ) + N 3 ,

(45) y 4 ( t s 4 ) = h 4 r 2 x s r 2 ( t s 4 ) + N 4 .

The decoded SINRs at UE 2 , UE 3 , and UE 4 are given by Eqs. (46)–(49).

(46) SINR t s 4 4 − 2 = ( 1 − ρ ) η ρ P 4 t s 4 P s 2 ( ∣ h r 2 BS ∣ 2 ) 2 ∣ h 2 r 2 ∣ 2 ( 1 − ρ ) η ρ P 2 t s 4 P s 2 ( ∣ h r 2 BS ∣ 2 ) 2 ∣ h 2 r 2 ∣ 2 + ( 1 − ρ ) P s ∣ h r 2 BS ∣ 2 σ 2 2 + σ R 2 2 σ 2 2 ,

(47) SINR t s 4 2 − 2 = ( 1 − ρ ) η ρ P 2 t s 4 P s 2 ( ∣ h r 2 BS ∣ 2 ) 2 ∣ h 2 r 2 ∣ 2 ( 1 − ρ ) P s ∣ h r 2 BS ∣ 2 σ 2 2 + σ R 2 2 σ 2 2 ,

(48) SINR t s 4 3 − 3 = ( 1 − ρ ) η ρ P 3 t s 4 P s 2 ( ∣ h r 1 BS ∣ 2 ) 2 ∣ h 3 r 1 ∣ 2 ( 1 − ρ ) P s ∣ h r 1 BS ∣ 2 σ 3 2 + σ R 1 2 σ 3 2 ,

(49) SINR t s 4 4 − 4 = ( 1 − ρ ) P 4 t s 4 η ρ P s 2 ( ∣ h r 2 BS ∣ 2 ) 2 ∣ h 4 r 2 ∣ 2 ( 1 − ρ ) η ρ P 2 t s 4 P s 2 ( ∣ h r 2 BS ∣ 2 ) 2 ∣ h 4 r 2 ∣ 2 + ( 1 − ρ ) P s ∣ h r 2 BS ∣ 2 σ 4 2 + σ R 2 2 σ 4 2 .

3 Energy-harvesting outage probability

The outage probability for energy harvesting is similar to that presented in ref. [11]. For generality, the conditions for communication interruption or an outage event may occur if one of the following conditions hold:

  1. If a user cannot detect the signals of higher-powered users.

  2. If a relay cannot detect the signals of higher-powered users.

  3. If a relay cannot detect the signals of the users connected to it.

  4. If the user throughput is not able to achieve the target rate

See reference [11] for more details.

3.1 Outage probability for UE 1

Outage probability for UE 1 in t s 1 :

(50) P 1 , t s 1 = P r [ OE 1 , t s 1 ] = P r [ OE r 4 − 1 t s 1 ∪ OE r 3 − 1 t s 1 ∪ OE r 2 − 1 t s 1 ∪ OE r 1 − 1 t s 1 ] = 1 − [ 1 − F R r 4 − 1 t s 1 ( R ) ] [ 1 − F R r 3 − 1 t s 1 ( R ) ] [ 1 − F R r 2 − 1 t s 1 ( R ) ] [ 1 − F R r 1 − 1 t s 1 ( R ) ] ,

(51) P 1 , t s 1 = 1 − e − β t s 1 σ 2 λ 1 BS P s 1 P 1 t s 1 + 1 P 2 t s 1 − P 1 t s 1 β t s 1 + 1 P 3 t s 1 − ∑ j = 1 2 P j t s 1 β t s 1 + 1 P 4 t s 1 − ∑ j = 1 3 P j t s 1 β t s 1 , 0 < β t s 1 < P 4 t s 1 ∑ j = 1 3 P j t s 1 ∪ P 3 t s 1 ∑ j = 1 2 P j t s 1 ∪ P 2 t s 1 P 1 t s 1 1 , else .

Outage probability for UE 1 in t s 3 :

(52) P 1 , t s 3 = P r [ OE 1 , t s 3 ] = P r [ OE r 3 − 1 t s 3 ∪ OE r 4 − 1 t s 3 ∪ OE r 2 − 1 t s 3 ∪ OE r 1 − 1 t s 3 ] = 1 − [ 1 − F R r 3 − 1 t s 3 ( R ) ] [ 1 − F R r 4 − 1 t s 3 ( R ) ] [ 1 − F R r 2 − 1 t s 3 ( R ) ] [ 1 − F R r 1 − 1 t s 3 ( R ) ] ,

(53) P 1 , t s 3 = 1 − e − β t s 3 σ 2 λ 1 B S P s 1 P 1 t s 3 + 1 P 2 t s 3 − P 1 t s 3 β t s 3 + 1 P 3 t s 3 − ∑ j = 1 2 P j t s 3 + P 4 t s 3 β t s 3 + 1 P 4 t s 3 − ∑ j = 1 2 P j t s 3 β t s 3 , 0 < β t s 3 < P 4 t s 3 ∑ j = 1 2 P j t s 3 ∪ P 3 t s 3 ∑ j = 1 2 P j t s 3 + P 4 t s 3 ∪ P 2 t s 3 P 1 t s 3 1 , else .

3.2 Outage probability for UE 2

Outage probability for UE 2 in t s 1 :

(54) P 2 , t s 1 = P r [ OE 2 , t s 1 ] = P r [ OE r 4 − 2 t s 1 ∪ OE r 3 − 2 t s 1 ∪ OE r 2 − 2 t s 1 ] = 1 − [ 1 − F R r 4 − 2 t s 1 ( R ) ] [ 1 − F R r 3 − 2 t s 1 ( R ) ] [ 1 − F R r 2 − 2 t s 1 ( R ) ] ,

(55) P 2 , t s 1 = 1 − e − β t s 1 σ 2 λ 2 BS P s 1 P 2 t s 1 − P 1 t s 1 β t s 1 + 1 P 3 t s 1 − ∑ j = 1 2 P j t s 1 β t s 1 + 1 P 4 t s 1 − ∑ j = 1 3 P j t s 1 β t s 1 , 0 < β t s 1 < P 4 t s 1 ∑ j = 1 3 P j t s 1 ∪ P 3 t s 1 ∑ j = 1 2 P j t s 1 ∪ P 2 t s 1 P 1 t s 1 1 , else .

Outage probability for UE 2 in t s 3 and t s 4 :

(56) P 2 , t s 4 = P r [ OE 2 , t s 4 ] = P r [ OE r 3 − r 2 t s 3 ∪ OE r 4 − r 2 t s 3 ∪ OE r 2 − r 2 t s 3 ∪ OE r 4 − 2 t s 4 ∪ OE r 2 − 2 t s 4 ] = 1 − [ 1 − F R r 3 − r 2 t s 3 ( R ) ] [ 1 − F R r 4 − r 2 t s 3 ( R ) ] [ 1 − F R r 2 − r 2 t s 3 ( R ) ] [ 1 − F R r 4 − 2 t s 4 ( R ) ] [ 1 − F R r 2 − 2 t s 4 ( R ) ] ,

(57) P 2 , t s 4 = 1 − e − λ r 2 BS P s σ 2 β t s 4 η ρ ∣ h 2 r 2 ∣ 2 1 P 2 t s 4 + 1 [ P 4 t s 4 − P 2 t s 4 β t s 4 ] + β t s 3 1 [ P 2 t s 3 − P 1 t s 3 β t s 3 ] + 1 P 4 t s 3 − ∑ j = 1 2 P j t s 3 β t s 3 + 1 P 3 t s 3 − ∑ j = 1 2 P j t s 3 + P 4 t s 3 β t s 3 , 0 < β t s 4 < P 4 t s 4 P 2 t s 4 ∪ β t s 3 < P 2 t s 3 P 1 t s 3 ∪ P 4 t s 3 ∑ j = 1 2 P j t s 3 ∪ P 3 t s 3 ∑ j = 1 2 P j t s 3 + P 4 t s 3 1 , else .

3.3 Outage probability for UE 3

Outage probability for UE 3 in t s 1 and t s 2 :

(58) P 3 , t s 2 = P r [ OE 3 , t s 2 ] = P r [ OE r 4 − r 2 t s 1 ∪ OE r 3 − r 2 t s 1 ∪ OE r 3 − 3 t s 2 ] = 1 − [ 1 − F R r 4 − r 2 t s 1 ( R ) ] [ 1 − F R r 3 − r 2 t s 1 ( R ) ] [ 1 − F R r 3 − 3 t s 2 ( R ) ] ,

(59) P 3 , t s 2 = 1 − e − σ 2 β t s 2 λ 3 r 2 P s η ρ P 3 t s 2 ∣ h r 2 BS ∣ 2 + β t s 1 λ r 2 B S P s 1 P 3 t s 1 − ∑ j = 1 2 P j t s 1 β t s 1 + 1 P 4 t s 1 − ∑ j = 1 3 P j t s 1 β t s 1 , 0 < β t s 2 ∪ β t s 1 < P 3 t s 1 ∑ j = 1 2 P j t s 1 ∪ P 4 t s 1 ∑ j = 1 3 P j t s 1 1 , else .

Outage probability for UE 3 in t s 3 and t s 4 :

(60) P 3 , t s 4 = P r [ OE 3 , t s 4 ] = P r [ OE r 3 − r 1 t s 3 ∪ OE r 3 − 3 t s 4 ] = 1 − [ 1 − F R r 3 − r 1 t s 3 ( R ) ] [ 1 − F R r 3 − r 1 t s 3 ( R ) ] ,

(61) P 3 , t s 4 = 1 − e − σ 2 β t s 4 λ 3 r 1 P s [ η ρ P 3 t s 4 ∣ h r 1 BS ∣ 2 ] + β t s 3 λ r 1 BS P s 1 P 3 t s 3 − ∑ j = 1 2 P j t s 3 + P 4 t s 3 β t s 3 , 0 < β t s 4 ∪ β t s 3 < P 3 t s 3 ∑ j = 1 2 P j t s 3 + P 4 t s 3 1 , else .

3.4 Outage probability for UE 4

Outage probability for UE 4 in t s 1 and t s 2 :

(62) P 4 , t s 2 = P r [ OE 4 , t s 2 ] = P r [ OE r 4 − r 1 t s 1 ∪ OE r 4 − 4 t s 2 ] = 1 − [ 1 − F R r 4 − r 1 t s 1 ( R ) ] [ 1 − F R r 4 − 4 t s 2 ( R ) ] ,

(63) P 4 , t s 2 = 1 − e − σ 2 β t s 2 λ 4 r 1 P s η ρ P 4 t s 2 ∣ h r 1 B S ∣ 2 + β t s 1 λ r 1 B S P s 1 P 4 t s 1 − ∑ j = 1 3 P j t s 1 β t s 1 , 0 < β t s 2 ∪ β t s 1 < P 4 t s 1 ∑ j = 1 3 P j t s 1 1 , else .

Outage probability for UE 4 in t s 3 and t s 4 :

(64) P 4 , t s 4 = P r [ OE 4 , t s 4 ] = P r [ OE r 3 − r 2 t s 3 ∪ OE r 4 − r 2 t s 3 ∪ OE r 4 − 4 t s 4 ] = 1 − [ 1 − F R r 3 − r 2 t s 3 ( R ) ] [ 1 − F R r 4 − r 2 t s 3 ( R ) ] [ 1 − F R r 4 − 4 t s 4 ( R ) ] ,

(65) P 4 , t s 4 = 1 − e − σ 2 β t s 4 λ 4 r 2 P s η ρ ∣ h r 2 BS ∣ 2 1 [ P 4 t s 4 − P 2 t s 4 β t s 4 ] + β t s 3 λ r 2 BS P s 1 P 4 t s 3 − ∑ j = 1 2 P j t s 3 β t s 3 + 1 P 3 t s 3 − ∑ j = 1 2 P j t s 3 + P 4 t s 3 β t s 3 , 0 < β t s 4 < P 4 t s 4 P 2 t s 4 ∪ β t s 3 < P 4 t s 3 ∑ j = 1 2 P j t s 3 ∪ P 3 t s 3 ∑ j = 1 2 P j t s 3 + P 4 t s 3 1 , else .

4 Simulation results

The simulation model is shown in Figures 1 and 2, with the energy-harvesting relay nodes. The system model has one BS, two relays ( r 1 and r 2 ) , and four users ( UE 1 , UE 2 , UE 3 , and UE 4 ) . The relay works in half-duplex mode. For t s 1 and t s 2 time sub-slots, UE 1 and UE 2 are cell centre users, while UE 3 and UE 4 are cell edge users using relays r 2 and r 1 . For t s 3 and t s 4 time sub-slots, UE 1 is a cell centre user, while UE 2 , UE 3 , and UE 4 are cell edge users. The UE 2 and UE 2 are connected to relay r 2 and UE 3 is connected to relay r 1 . The relays harvest energy from the received signal and employ the AF protocol to forward the intended signals to the connected users. The system parameters for the energy-harvesting non-orthogonal multiple access (NOMA)-based system are given in Table 1. Simulation results compare the four-user NOMA-based network proposed by ref. [11] with and with energy-harvesting relay capabilities.

Table 1

System parameters

P s = 25 − 50 dB Base station power
λ 1 BS = 1 − 4 , λ 2 BS = 0.8 − 4 , λ r 1 BS = 0.4 − 4 , λ r 2 BS = 0.5 − 4 , λ 3 r 2 = 0.3 − 4 , λ 4 r 1 = 0.3 − 4 Figure 1 channel variances
λ 1 BS = 1 − 4 , λ r 1 BS = 0.4 − 4 , λ r 2 BS = 0.5 − 4 , λ 2 r 2 = 0.3 − 4 , λ 3 r 1 = 0.3 − 4 , λ 4 r 2 = 0.4 − 4 Figure 2 channel variances
R = 0.3 bps/Hz Target rate
ρ = 0.5 Power splitting coefficient
η = 1 Energy conversion efficiency
P s = 10 − 20 dB Transmit power

The simulation results show the outage probability of UEs in the various time sub-slots. Figure 3 shows the outage probability of UE 1 in t s 1 and t s 3 , with and without energy-harvesting relays. The energy harvesting does not affect UE 1 as it is always a cell-centre user and connects directly to the base station. The figure also shows a slight change in the outage probability of UE 1 from t s 1 to t s 3 .

Figure 3 Outage probability of user 1.
Figure 3

Outage probability of user 1.

Figure 4 shows the outage probability of UE 2 in t s 1 and t s 3 − 4 . During time sub-slot 1, UE 2 is a cell centre user, and therefore the energy harvesting does not affect this user. However, for time sub-slot t s 3 − 4 , the outage probability of UE 2 improves; because UE 2 is a cell-edge user and connected to an energy harvesting relay.

Figure 4 Outage probability of user 2.
Figure 4

Outage probability of user 2.

Figures 5 and 6 show the outage probability of UE 3 and UE 4 , respectively. These UEs are cell edge users in both time slots; therefore, they benefit from the energy-harvesting relays where their outage probabilities improve. The change in positions shows a noticeable difference between the outage probability of UE 3 and UE 4 . For the first time slot ( t s 1 − 2 ) , UE 3 is connected to relay 2 with the second highest allocated power, whereas UE 4 is connected to relay 1 with the highest allocated power. However, in time slot ( t s 3 − 4 ) , UE 3 is connected to relay 1 with the highest allocated power and UE 4 shares a relay with UE 2 .

Figure 5 Outage probability of user 3.
Figure 5

Outage probability of user 3.

Figure 6 Outage probability of user 4.
Figure 6

Outage probability of user 4.

5 Conclusion

This article evaluated the effectiveness of the energy-harvesting relay nodes on the user’s outage probability. The four-user NOMA-based network utilises energy-harvesting relays to communicate with the base station. This research is an adaptation and extension of the research presented by ref. [11], utilising the same methods and procedures to derive the outage probability expressions. The results simply show the impact of the energy harvesting on the outage probability of the users as well as their positions in the network. The cell edge users connected to the relays benefit from the harvested energy by receiving more power than the network without harvesting, which can be seen in the results. Future works may include the physical layer security of the energy-harvesting network by implementing a jamming signal to mitigate eavesdropping.

  1. Funding information: The authors state no funding involved.

  2. Author contributions: All authors have accepted responsibility for the entire content of this manuscript and approved its submission.

  3. Conflict of interest: The authors state no conflict of interest.

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Received: 2022-04-15
Revised: 2022-07-29
Accepted: 2022-08-15
Published Online: 2022-12-21

© 2022 the author(s), published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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https://doi.org/10.1515/nleng-2022-0240
Keywords for this article
NOMA; energy harvesting; power splitting protocol; amplify-and-forward; outage probability
Creative Commons
BY 4.0

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