Throughput analysis of non-orthogonal multiple access and orthogonal multiple access assisted wireless energy harvesting K-hop relaying networks

Throughput analysis of non-orthogonal multiple access and orthogonal multiple access assisted wireless energy harvesting K-hop relaying networks

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  International Journal ofElectrical and Computer Engineering (IJECE) Vol. 13, No. 1, February 2023, pp. 522~530 ISSN: 2088-8708, DOI: 10.11591/ijece.v13i1.pp522-530  522 Journal homepage: http://ijece.iaescore.com Throughput analysis of non-orthogonal multiple access and orthogonal multiple access assisted wireless energy harvesting K-hop relaying networks Phung Ton That1 , Nhat-Tien Nguyen2 , Duy-Hung Ha3 , Miroslav Voznak2 1 Faculty of Electronics Technology, Industrial University of Ho Chi Minh City, Ho Chi Minh City, Vietnam 2 Faculty of Electrical Engineering and Computer Science, VSB-Technical University of Ostrava, Ostrava, Czech Republic 3 Wireless Communications Research Group, Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam Article Info ABSTRACT Article history: Received Apr 7, 2022 Revised Oct 7, 2022 Accepted Oct 18, 2022 This study introduces the non-orthogonal multiple access (NOMA) technique into the wireless energy harvesting K-hop relay network to increase throughput. The relays have no dedicated energy source and thus depend on energy harvested by wireless from a power beacon (PB). Recently, NOMA has been promoted as a technology with the potential to enhance connectivity, reduce latency, increase fairness amongst users, and raise spectral effectiveness compared to orthogonal multiple access (OMA) technology. For performance considerations, we derive exact throughput expressions for NOMA and OMA-assisted multi-hop relaying and compare the performance between the two. The obtained results are validated via Monte Carlo simulations. Keywords: Decode-and-forward Multi-hop Non-orthogonal multiple access Power beacon Relays Throughput Wireless energy harvesting This is an open access article under the CC BY-SA license. Corresponding Author: Duy-Hung Ha Wireless Communications Research Group, Faculty of Electrical and Electronics Engineering, Ton Duc Thang University Ho Chi Minh city, Vietnam Email: [email protected] 1. INTRODUCTION Wireless energy harvesting enables the development of new devices for internet-of-medical things (IoMT), wireless sensor networks (WSNs), infrastructure and environmental monitoring and surveillance where battery-powered devices would be unsuitable [1]–[3]. In addition, energy harvesting enables energy sufficiency and lifetime operation for devices placed within building materials and the human body [1]. The potential application for wireless energy harvesting is relay networks, where the source transmit power during the uplink functions as an arbitrary variable in wireless powered communication network (WPCN) because of the intrinsic power transmission. Due to the dramatic increase of battery-powered communication devices, the goal of extending their life is very important, and the highest throughput in the shortest amount of time, a good allocation of uplink and downlink times were calculated by [4], [5]. For example, in a wide- body area network (WBAN), or IoMT, the relays depend on a reliable and perpetual source of energy since battery replacement would be undesirable [4], [6]. There are various types of natural sources for harvesting, such as thermal, chemical, and vibration. In this paper, we consider harvesting energy from a power beacon (PB) based on the time switching protocol [7]–[9]. Hence, the source node transmits its data via relays, and every node makes use of the harvested PB energy for data transmission [10], [11]. As a result, K-hop relaying networks can provide line-of-sight (LoS) in obstruction filled environments such as indoor networks [12].
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  Int J Elec& Comp Eng ISSN: 2088-8708  Throughput analysis of non-orthogonal multiple access and orthogonal … (Phung Ton That) 523 However, a fundamental problem faced by wireless energy harvesting multi-hop relaying network is the issue of throughput. Tian et al. [13] developed an optimal throughput broadcast algorithm to deal with the stochastic nature of the source and energy collection at the relays. In [14]–[16], a throughput algorithm is designed to acquire solutions to the optimal time and non-convex power distribution problem in wireless energy-harvesting cognitive radio networks. The authors in [17]–[19] investigated wireless powered communication networks assisted by non-orthogonal multiple access (NOMA), where signal is transmitted to a sink node, and the sink utilizes successive interference cancellation (SIC) to remove interference at its receivers. NOMA is viewed as a viable candidate to increase connectivity and spectral effectiveness than traditional orthogonal multiple access (OMA) methods in emerging wireless networks by exploiting SIC and superposition coding to enable more user connectivity with no interference [20]–[22]. Internet of thing (IoT) security is a challenge due to limitations in connectivity, form factor, complexity, and power. Recently, many studies have been proposed for physical layer security (PLS) techniques in the fifth generation (5G); however, due to complex limitations, some of these solutions cannot be applied in IoT networks. NOMA is considered a viable technology to solve latency and connectivity requirements in IoT [23]–[27]. In [28]–[31], the authors have applied a NOMA with implementation of signal processing on the downlink side. A nearby user can be a relay to transfer the signal to the far user by taking advantage of the benefits of full-duplex mode, allowing the relay to transmit and receive signals at the same time. For efficient data transmission, the shadowing and fading effects of the channels also play an important role [32]–[34]. Additionally, reconfigurable intelligent surfaces (RIS) is an emerging technology that is combined with multiple antennas-aided wireless systems with the presence of NOMA to the assistance improvement of far user performance [35], [36]. Motivated by the above ideas, we analyze a proposed wireless energy harvesting multi-hop decode and-forward relay network assisted NOMA. The main contributions of this study are i) compared with the system model and mathematical formula reported in [17], this paper proposes relays operating in half-duplex mode and ii) we derive exact throughput analytical expressions for NOMA assisted wireless energy harvesting multi-hop networks, as well as for the OMA case, and compare the throughput performance using simulation results. The closed-form throughput results are verified by Monte Carlo simulations. The rest of this work is organized in the following way: section 2 describes the recommended system parameters. Then, in section 3, we derive the exact results of the throughput for the NOMA and OMA cases. We highlight the results in section 4, and give an important results summary in section 5. 2. SYSTEM MODEL As shown in Figure 1, the source-𝑇0 transmits information to the destination-𝑇𝐾 through 𝐾 − 1 relays are said to be 𝑇1, 𝑇2, … , 𝑇𝐾−1. The transmitter 𝑇𝐾 harvests energy from the PB to supply energy for its decode-and-forward (DF) actions, where 𝑘 = 0,1, … , 𝐾 − 1. All nodes in our system have a single antenna. Therefore, K orthogonal time slots are used for information transmission. Figure 1. A 𝐾-hop DF relay network with energy collection from PB functionality We define 𝒬 as the time for end-to-end transmission. Thus, the dedicated time slot for data transmission is 𝜏 = 𝒬/𝐾. In addition, a portion of the time slot  is dedicated for energy harvesting from
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   ISSN: 2088-8708 IntJ Elec & Comp Eng, Vol. 13, No. 1, February 2023: 522-530 524 the PB, and the remainder (1 − 𝑎)𝜏 is used for decoding and forwarding operations, where 0 1    represents the block time portion. Thus, the harvest energy by 𝑇𝐾 is written as [20]. 𝐸 ̄𝑘 = 𝜂𝛼𝜏𝑃 ̄𝑃ℎ ̄𝑃𝑘 (1) where ( ) 0 1    is the energy conversion efficiency, 𝑃 ̅𝑃 is the power of PB transmitter, ℎ ̅𝑃𝑘 represents the channel between PB and 𝑇𝐾. From (1), the 𝑇𝐾 transmitter power is obtained as (2) [37]: 𝑃 ̄𝑘 = 𝐸 ̄𝑘 (1−𝛼)𝜏 = 𝛿𝑃 ̄𝑃ℎ ̄𝑃𝑘 (2) where 𝛿 = 𝜂𝛼 1−𝛼 . Remark 1: To simplify our calculations, we assume that the energy harvesting operates on different frequencies to the data transmission process, thus, preventing interference at the relay receivers. We consider that in the 𝑘-th time slot, node 𝑇𝑘−1 transmits data to node 𝑇𝐾, where 𝑘 = 1, . . . , 𝐾. To improve throughput, the relay 1 k T − uses superposition coding to combine N signals to produce a superimposed signal expressed as (3). 𝑥̄ = ∑ √𝑎𝑛𝑃 ̄𝑘−1𝑥̄𝑛 𝑁 𝑛=1 (3) with for 𝑛 = 1,2, . . . , 𝑁; 𝑎𝑛 represents the power allocation coefficients, ∑ 𝑎𝑛 = 1 𝑁 𝑛=1 and 𝑎1 > 𝑎2 >. . . > 𝑎𝑁; 𝑥̄𝑛 is the transmitted signal. Remark 2: Traditionally, OMA has been the backbone of 𝐾-hop relaying resulting in a data rate of 1/𝐾. Thus, by superposing 𝑁 signals, our proposed scheme's data rate is 𝑁/𝐾. Assuming perfect successive interference cancellation (pSIC) [21], [22], [38], [39], the 𝑇𝐾 the transmit signal-to-noise ratio (SNR) for decoding n x under hardware impairments can be written as (4) [40]: 1 2 1 1 0 1 1 2 0 if if = n k Dk N k D i k D k k i n N k Dk k Dk a P h n N P h a P h N n k a P h n N P h N − − − = + −  + + +     =        (4) where ℎ ̄𝐷𝑘 is the channel gain between 𝑇𝑘−1 and 𝑇𝐾, 𝐾2 is the combined hardware impairment [41]–[43], and 𝑁0 is the additive white gaussian noise (AWGN). Substituting (2) into (5) yields. 1 2 1 1 1 2 1 1 1 if if = n P D k k N i P D k k i n N P D k k P D k k a h h n N a h h n k a h h n N h h − − = + − −         +  +         +       =      (5) Where 0 / P P N  = is the transmit SNR. Furthermore, the instantaneous channel capacity of n x is obtained as (6). 𝐶 ̄𝑘 𝑛 = (1 − 𝛼)𝜏 𝑙𝑜𝑔2 (1 + 𝜓 ̄𝑘 𝑛 ). (6) The channel capacity of 𝑥̄𝑛 with DF relaying as (7).
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  Int J Elec& Comp Eng ISSN: 2088-8708  Throughput analysis of non-orthogonal multiple access and orthogonal … (Phung Ton That) 525 𝐶 ̄e2e 𝑛 = 𝑚𝑖𝑛 𝑘=1,2,...,𝐾 (𝐶 ̄𝑘 𝑛 ). (7) Finally, we can define the throughput similar to [4], [14] as (8). 𝑇NOMA = (1 − 𝛼)𝜏𝛾̄𝑡ℎ ∑ 𝑃𝑟(𝐶 ̄e2e 𝑛 ≥ 𝛾̄𝑡ℎ) 𝑁 𝑛=1 (8) where 𝛾̄𝑡ℎ is desired target rate. We also consider the 𝐾-hop relaying with OMA. Here, 𝑇𝑘−1 uses power 𝑃 ̄𝑘−1 to transmit one signal to 𝑇𝐾. Therefore, the throughput becomes [44]: 𝑇OMA = (1 − 𝛼)𝜏𝛾th 𝑃𝑟(𝐶 ̄e2e OMA ≥ 𝛾̄𝑡ℎ) (9) where 𝐶 ̄e2e OMA = 𝑚𝑖𝑛 𝑘=1,2,...,𝐾 ((1 − 𝛼)𝜏 log2 (1 + 𝜌𝛿ℎ ̄𝑃𝑘−1 ℎ ̄𝐷𝑘 𝜅2𝜌𝛿ℎ ̄𝑃𝑘−1 ℎ ̄𝐷𝑘 +1 )). (10) 3. THROUGHPUT ECALUATION 3.1. Nakagami-𝒎 fading channel model We assume the system channels follow Nakagami-𝑚 fading also that the channel gains ℎ ̅𝑃𝑘 and ℎ ̅𝐷𝑘 are exponential random variables (RVs). We define Ω𝑃𝑘 and Ω𝐷𝑘 as the RVs channel parameters. Thus, cumulative distribution functions (CDFs) of the ℎ ̅𝑃𝑘 and ℎ ̅𝐷𝑘 can be written by [45], respectively as in (11) and (12). 𝐹ℎ ̄𝑃𝑘 (𝑥) = 1 − 𝑒 − 𝑥 𝛽𝑃𝑘 ∑ 𝑥𝑛 𝑛!𝛽𝑃𝑘 𝑛 𝑚𝑃𝑘 −1 𝑛=0 𝑛 (11) 𝐹ℎ ̄𝐷𝑘 (𝑥) = 1 − 𝑒 − 𝑥 𝛽𝐷𝑘 ∑ 𝑥𝑛 𝑛!𝛽𝐷𝑘 𝑛 𝑚𝐷𝑘 −1 𝑛=0 . (12) Therefore, the probability density functions (PDF) of ℎ ̅𝑃𝑘 and ℎ ̅𝐷𝑘 are obtained as [46]: 𝑓ℎ ̄𝑃𝑘 (𝑥) = 𝑥 𝑚𝑃𝑘 −1 𝛤(𝑚𝑃𝑘 )𝛽𝑃𝑘 𝑚𝑃𝑘 𝑒 − 𝑥 𝛽𝑃𝑘 (13) 𝑓ℎ ̄𝐷𝑘 (𝑥) = 𝑥 𝑚𝐷𝑘 −1 𝛤(𝑚𝐷𝑘 )𝛽𝐷𝑘 𝑚𝐷𝑘 𝑒 − 𝑥 𝛽𝐷𝑘 (14) where 𝛽𝑧 ≜ 𝛺𝑧 𝑚𝑧 , 𝑧 ∈ (𝑃𝑘; 𝐷𝑘). Taking the path loss into account, the channel parameters Ω𝑃𝑘 and Ω𝐷𝑘 can be modeled as (15) [47]: 𝛺𝑃𝑘 = 𝑑𝑃𝑘 −𝜀 , 𝛺𝐷𝑘 = 𝑑𝐷𝑘 −𝜀 (15) where d𝑃𝑘 and d𝐷𝑘 are the distances of 𝑃𝑏 → 𝑇𝑘 and 𝑇𝑘 → 𝑇𝑘+1, respectively, the path-loss exponent is denoted by 𝜀, Ω𝑃𝑘 and 𝑚𝑧 denote the mean and the integer fading factor. 3.2. NOMA throughput analysis Firstly, we calculate the probability 𝑃𝑟(𝐶̅𝑒2𝑒 𝑛 ≥ 𝛾𝑡ℎ). Taking 𝑛 < 𝑁 and combining (5) to (7), we obtain (16). 𝑃𝑟(𝐶 ̄e2e 𝑛 ≥ 𝛾𝑡ℎ) = ∏ 𝑃𝑟(𝐶 ̄𝑘 𝑛 ≥ 𝛾𝑡ℎ) 𝐾 𝑘=1 = ∏ 𝑃𝑟 ( 𝜌𝑎𝑛𝛿ℎ ̄𝑃𝑘−1 ℎ ̄𝐷𝑘 (𝜅2+∑ 𝑎𝑖 𝑁 𝑖=𝑛+1 )𝜌𝛿ℎ ̄𝑃𝑘−1 ℎ ̄𝐷𝑘 +1 ≥ 𝜃) 𝐾 𝑘=1 (16)
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   ISSN: 2088-8708 IntJ Elec & Comp Eng, Vol. 13, No. 1, February 2023: 522-530 526 where 𝜃 = 2 𝛾𝑡ℎ (1−𝑎)𝜏 − 1 is the SINR threshold. It is obvious from (16) that if 𝛼𝑛 − 𝜃(𝜅2 + ∑ 𝛼𝑖 𝑁 𝑖=𝑛+1 ) ≤ 0 then 𝑃𝑟(𝐶̅𝑒2𝑒 𝑛 ≥ 𝛾𝑡ℎ) = 0, and if 𝛼𝑛 − 𝜃(𝜅2 + ∑ 𝛼𝑖 𝑁 𝑖=𝑛+1 ) > 0, (16) becomes: 𝑃𝑟(𝐶 ̄e2e 𝑛 ≥ 𝛾𝑡ℎ) = ∏ 𝑃𝑟 𝐾 𝑘=1 (ℎ ̄𝑃𝑘−1 ℎ ̄𝐷𝑘 ≥ 𝜎̄𝑛) (17) where 𝜎̄𝑛 = 𝜃 [𝑎𝑛−(𝜅2+∑ 𝑎𝑖 𝑁 𝑖=𝑛+1 )𝜃]𝜌𝛿 . (18) Remark 3: The transmit power ratio 𝛼𝑛 must be carefully designed so that the conditions, i.e., 𝛼𝑛 − 𝜃(𝜅2 + ∑ 𝛼𝑖 𝑁 𝑖=𝑛+1 ) > 0, are satisfied. Now, the probability 𝑃𝑟(ℎ ̄𝑃𝑘−1 ℎ ̄𝐷𝑘 ≥ 𝜎̄𝑛) can be formulated by (19). 𝑃𝑟(ℎ ̄𝑃𝑘−1 ℎ ̄𝐷𝑘 ≥ 𝜎̄𝑛) = ∫ (1 − 𝐹ℎ ̄𝑃𝑘−1 ( 𝜎̄𝑛 𝑥 )) +∞ 0 𝑓ℎ ̄𝐷𝑘 (𝑥)𝑑𝑥. (19) Putting (11) to (14) in (19), and then using [48], (3.471.9), we get (20). 𝑃𝑟(𝐶 ̄e2e 𝑛 ≥ 𝛾𝑡ℎ) = ∏ [∫ (1 − 𝐹𝑃𝑘−1 ( 𝜎̄𝑛 𝑥 )) ∞ 0 𝑓𝐷𝑘 (𝑥)𝑑𝑥] 𝐾 𝑘=1 = ∏ [ ∑ 𝜎̄𝑛 𝑙 𝑙! 𝛽𝑃𝑘−1 𝑙 𝛤(𝑚𝐷𝑘 )𝛽𝐷𝑘 𝑚𝐷𝑘 𝑚𝑃𝑘−1 −1 𝑙=0 𝐾 𝑘=1 × ∫ 𝑒 − 𝜎̄𝑛 𝛽𝑃𝑘−1 𝑥 − 𝑥 𝛽𝐷𝑘 ∞ 0 𝑥𝑚𝐷𝑘 −𝑙−1 𝑑𝑥] = ∏ [∑ 2𝜌𝑛 𝑙 𝑙!𝛽𝑃𝑘−1 𝑙 𝛤(𝑚𝐷𝑘 )𝛽𝐷𝑘 𝑚𝐷𝑘 𝑚𝑃𝑘−1 −1 𝑙=0 𝐾 𝑘=1 × ( 𝛽𝐷𝑘 𝜎̄𝑛 𝛽𝑃𝑘−1 ) 𝑚𝐷𝑘 −𝑙 2 𝐾𝑚𝐷𝑘 −𝑙 (2√ 𝜎̄𝑛 𝛽𝑃𝑘−1 𝛽𝐷𝑘 )] (20) Where 𝐾𝑢(. ) stands for the 𝑢𝑡ℎ order of the modified Bessel function of the second kind [48], (3.471.9). Similarly, when 𝑛 = 𝑁 we get (21). 𝑃𝑟(𝐶 ̄e2e 𝑁 ≥ 𝛾𝑡ℎ) = ∏ [∑ 2𝜎̄𝑁 𝑙 𝑙!𝛽𝑃𝑘−1 𝑙 𝛤(𝑚𝐷𝑘 )𝛽𝐷𝑘 𝑚𝐷𝑘 𝑚𝑃𝑘−1 −1 𝑙=0 𝐾 𝑘=1 × ( 𝛽𝐷𝑘 𝜎̄ 𝑁 𝛽𝑃𝑘−1 ) 𝑚𝐷𝑘 −𝑙 2 𝐾𝑚𝐷𝑘 −𝑙 (2√ 𝜎̄ 𝑁 𝛽𝑃𝑘−1 𝛽𝐷𝑘 )] (21) Where 𝜎̄𝑁 = 𝜃 (𝑎𝑁−𝜅2𝜃)𝜌𝛿 . Inserting (8), (20) and (21) together, an exact closed-form formula of 𝑇NOMA is acquired as (22). 𝑇NOMA = (1 − 𝛼)𝜏𝛾𝑡ℎ × {∑ ∏ [∑ 2𝜎̄𝑁 𝑙 𝑙!𝛽𝑃𝑘−1 𝑙 𝛤(𝑚𝐷𝑘 )𝛽𝐷𝑘 𝑚𝐷𝑘 𝑚𝑃𝑘−1 −1 𝑙=0 𝐾 𝑘=1 𝑁 𝑛=1 × ( 𝛽𝐷𝑘 𝜎̄ 𝑁 𝛽𝑃𝑘−1 ) 𝑚𝐷𝑘 −𝑙 2 𝐾𝑚𝐷𝑘 −𝑙 (2√ 𝜎̄ 𝑁 𝛽𝑃𝑘−1 𝛽𝐷𝑘 )]}. (22) 3.3. OMA throughput analysis For multi-hop relaying using OMA, we get 𝑃𝑟(𝐶 ̄e2e OMA ≥ 𝛾𝑡ℎ) = ∏ 𝑃𝑟(ℎ ̄𝑃𝑘−1 ℎ ̄𝐷𝑘 ≥ 𝜉 ̄) 𝐾 𝑘=1 = ∏ [∑ 2𝜉 ̄ 𝑙 𝑙!𝛽𝑃𝑘−1 𝑙 𝛤(𝑚𝐷𝑘 )𝛽𝐷𝑘 𝑚𝐷𝑘 𝑚𝑃𝑘−1 −1 𝑙=0 𝐾 𝑘=1 × ( 𝛽𝐷𝑘 𝜉 ̄ 𝛽𝑃𝑘−1 ) 𝑚𝐷𝑘 −𝑙 2 𝐾𝑚𝐷𝑘 −𝑙 (2√ 𝜉 ̄ 𝛽𝑃𝑘−1 𝛽𝐷𝑘 )] (23) where 𝜉 ̄ = 𝜃 (1−𝜅2𝜃)𝜌𝛿 . From (23), the throughput 𝑇NOMA is expressed as (24).
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  Int J Elec& Comp Eng ISSN: 2088-8708  Throughput analysis of non-orthogonal multiple access and orthogonal … (Phung Ton That) 527 𝑇OMA = (1 − 𝛼)𝜏𝛾𝑡ℎ × ∏ [∑ 2𝜉 ̄ 𝑙 𝑙!𝛽𝑃𝑘−1 𝑙 𝛤(𝑚𝐷𝑘 )𝛽𝐷𝑘 𝑚𝐷𝑘 𝑚𝑃𝑘−1 −1 𝑙=0 𝐾 𝑘=1 × ( 𝛽𝐷𝑘 𝜉 ̄ 𝛽𝑃𝑘−1 ) 𝑚𝐷𝑘 −𝑙 2 𝐾𝑚𝐷𝑘 −𝑙 (2√ 𝜉 ̄ 𝛽𝑃𝑘−1 𝛽𝐷𝑘 )]. (24) 4. MUMERICAL RESULTS Here, we address the main parameters of Monte Carlo simulation. The source node is located at the origin (0, 0) and the destination at (1, 0), thus the distance between the source and the destination node is 1. Then, the coordinates of the relay Tk and the power beacon PB are (k / K, 0) and (0.5, 0.5), respectively, with k=1, 2, ..., K-1. We set 𝑚𝑃𝑘−1 = 𝑚𝑃𝑘 = 𝑚𝐷𝑘−1 = 𝑚𝐷𝑘 = 𝑚 = 2. Three NOMA schemes are considered as follows. In scheme I, we consider a1=0.85, a2=0.15, and N=2; in scheme II, we set a1=0.85, a2=0.12, a3=0.03, and N=3; and in scheme III, the parameters are an ∈ {0.85, 0.12, 0.025, 0.005}, with n=1,2,3,4, and N=4. Monte-Carlo results are averaged over 107 independent channel executions. Specifically, Table 1 shows the main parameters. Table 1. System parameters used in the throughput evaluation System Parameters Values The aggregate impairment level 𝜅2 = 0.01 Targeted data rate 𝛾̅𝑡ℎ = 0.1 The total transmission time 𝑄 = 1 Pass loss exponent 𝜀 = 3 The energy conversion efficiency 𝜂 = 1 The fraction of the block time 𝛼 = 0.1 Observe the relationship between throughput and transmit SNR shown in Figure 2 with parameters 𝑚 = 2, 𝜅2 = 0.01, 𝛼 = 0.1, and 𝐾 = 3, we found different throughput performance curves depending on 𝑁, the number of superposed signals, with NOMA-analytical 𝑁 = 4 has the best performance. Compared to OMA, NOMA outperforms OMA significantly in Figure 2. Observe the relationship between throughput and transmit SNR with parameters 𝜅2 = 0.01, 𝛼 = 0.1, and 𝐾 = 3. We see different throughput performance curves depending on Nakagami-m fading parameter 𝑚, with NOMA-analytical 𝑚 = 3 performing the best. Compared to OMA, NOMA outperforms OMA significantly in Figure 3. Furthermore, the throughput of OMA reaches a ceiling at transmitting SNR 𝜌 = 10 𝑑𝐵. In Figures 4, and 5, we can see the continued trend of NOMA outperforming OMA. However, in Figure 4, we observe the throughput reduction by adding of 𝐾-hops. Also, in Figure 5, we notice that throughput decreases drastically beyond the optimal 𝛼. This highlights the importance of designing optimal time-switching protocols. All analytical curves match well with the Monte Carlo simulation results. Figure 2. Throughput with 𝑚 = 2, 𝜅2 = 0.01, 𝛼 = 0.1 and 𝐾 = 3 Figure 3. Throughput with 𝜅2 = 0.01, 𝛼 = 0.1 and 𝐾 = 3
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   ISSN: 2088-8708 IntJ Elec & Comp Eng, Vol. 13, No. 1, February 2023: 522-530 528 Figure 4. Throughput with 𝜅2 = 0, 𝑚 = 3 and 𝜌 = 25 𝑑𝐵 Figure 5. Throughput with 𝐾 = 3, 𝜅2 = 0, 𝑚 = 3 and 𝜌 = 10 𝑑𝐵 5. CONCLUSION In this study, we provided a throughput analysis of NOMA assisted wireless energy harvesting multi-hop decode-and-forward network. We derived exact throughput expressions for the NOMA and OMA assistance. The results of simulation show that time switching and the number of relays play a significant role in throughput. We will consider a system that uses multiple power beacons in future work. ACKNOWLEDGEMENTS The research leading to these results was supported by the Ministry of Education, Youth and Sports of the Czech Republic under the grant SP2022/5 and e-INFRA CZ (ID: 90140). REFERENCES [1] S. Ulukus et al., “Energy harvesting wireless communications: A review of recent advances,” IEEE Journal on Selected Areas in Communications, vol. 33, no. 3, pp. 360–381, Mar. 2015, doi: 10.1109/JSAC.2015.2391531. [2] X. Lu, P. Wang, D. Niyato, D. I. Kim, and Z. Han, “Wireless networks with RF energy harvesting: A contemporary survey,” IEEE Communications Surveys & Tutorials, vol. 17, no. 2, pp. 757–789, 2015, doi: 10.1109/COMST.2014.2368999. [3] P. S. Lakshmi, M. G. Jibukumar, and V. S. Neenu, “Network lifetime enhancement of multi-hop wireless sensor network by RF energy harvesting,” in 2018 International Conference on Information Networking (ICOIN), Jan. 2018, pp. 738–743, doi: 10.1109/ICOIN.2018.8343216. [4] R. Fan, S. Atapattu, W. Chen, Y. Zhang, and J. Evans, “Throughput maximization for multi-hop decode-and-forward relay network with wireless energy harvesting,” IEEE Access, vol. 6, pp. 24582–24595, 2018, doi: 10.1109/ACCESS.2018.2831253. [5] R. M. Thomas and M. Subramani, “Multiuser-scheduling and resource allocation using max-min technique in wireless powered communication networks,” Indonesian Journal of Electrical Engineering and Computer Science (IJEECS), vol. 27, no. 2, pp. 832–841, Aug. 2022, doi: 10.11591/ijeecs.v27.i2.pp832-841. [6] M. Mao, N. Cao, Y. Chen, and Y. Zhou, “Multi-hop relaying using energy harvesting,” IEEE Wireless Communications Letters, vol. 4, no. 5, pp. 565–568, Oct. 2015, doi: 10.1109/LWC.2015.2462346. [7] V. N. Q. Bao, T. T. Duy, and N. T. Van, “Exact outage analysis of energy-harvesting multihop cluster-based networks with multiple power beacons over Nakagami-m fading channels,” in 2018 2nd International Conference on Recent Advances in Signal Processing, Telecommunications & Computing (SigTelCom), Jan. 2018, pp. 1–6, doi: 10.1109/SIGTELCOM.2018.8325769. [8] S. Atapattu, H. Jiang, J. Evans, and C. Tellambura, “Time-switching energy harvesting in relay networks,” in 2015 IEEE International Conference on Communications (ICC), Jun. 2015, pp. 5416–5421, doi: 10.1109/ICC.2015.7249185. [9] P. M. Nam, T.-L. Nguyen, H. D. Hung, T. T. Duy, N. T. Binh, and N. L. Nhat, “Throughput analysis of power beacon-aided multi-hop MIMO relaying networks employing NOMA and TAS/SC,” TELKOMNIKA (Telecommunication Computing Electronics and Control), vol. 20, no. 4, pp. 731–739, Aug. 2022, doi: 10.12928/telkomnika.v20i4.23769. [10] M.-S. Van Nguyen, P. H. Dang, and N. D. Nguyen, “Exploiting user grouping and energy harvesting in downlink cellular system,” Bulletin of Electrical Engineering and Informatics (BEEI), vol. 11, no. 2, pp. 870–877, Apr. 2022, doi: 10.11591/eei.v11i2.2982. [11] M.-S. Van Nguyen, T.-T. Nguyen, and D.-T. Do, “User grouping-based multiple access scheme for IoT network,” TELKOMNIKA (Telecommunication Computing Electronics and Control), vol. 19, no. 2, pp. 499–506, Apr. 2021, doi: 10.12928/telkomnika.v19i2.16181. [12] A.-T. Le, D.-T. Do, and M. Munochiveyi, “Outage performance of downlink NOMA-aided small cell network with wireless power transfer,” Bulletin of Electrical Engineering and Informatics (BEEI), vol. 10, no. 5, pp. 2686–2695, Oct. 2021, doi: 10.11591/eei.v10i5.3015. [13] X. Tian, B. Zhang, C. Li, and K. Hao, “Throughput-optimal broadcast for time-varying directed acyclic wireless multi-hop networks with energy harvesting constraints,” IEEE Transactions on Green Communications and Networking, vol. 5, no. 4, pp. 2089–2103, Dec. 2021, doi: 10.1109/TGCN.2021.3077708.
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   ISSN: 2088-8708 IntJ Elec & Comp Eng, Vol. 13, No. 1, February 2023: 522-530 530 [44] X. Wang, M. Jia, I. W.-H. Ho, Q. Guo, and F. C. M. Lau, “Exploiting full-duplex two-way relay cooperative non-orthogonal multiple access,” IEEE Transactions on Communications, vol. 67, no. 4, pp. 2716–2729, Apr. 2019, doi: 10.1109/TCOMM.2018.2890264. [45] D.-T. Do, T.-T. T. Nguyen, C.-B. Le, M. Voznak, Z. Kaleem, and K. M. Rabie, “UAV relaying enabled NOMA network with hybrid duplexing and multiple antennas,” IEEE Access, vol. 8, pp. 186993–187007, 2020, doi: 10.1109/ACCESS.2020.3030221. [46] D.-T. Do, T.-T. T. Nguyen, T. N. Nguyen, X. Li, and M. Voznak, “Uplink and downlink NOMA transmission using full-duplex UAV,” IEEE Access, vol. 8, pp. 164347–164364, 2020, doi: 10.1109/ACCESS.2020.3023163. [47] J. Jose, P. Shaik, and V. Bhatia, “VFD-NOMA under imperfect SIC and residual inter-relay interference over generalized Nakagami-m fading channels,” IEEE Communications Letters, vol. 25, no. 2, pp. 646–650, Feb. 2021, doi: 10.1109/LCOMM.2020.3030210. [48] I. S. Gradshteyn, I. M. Ryzhik, A. Jeffrey, and D. Zwillinger, Table of integrals, series, and products, 6th edition. Academic Press, 2000. BIOGRAPHIES OF AUTHORS Phung Ton That was born in Thua Thien-Hue, Viet Nam. He received the B.S. degree in electronics and telecommunications engineering (2007) and the M.S. degree in electronics engineering (2010) from the University of Technology, Vietnam. He is currently a lecturer at the Faculty of Electronics Technology (FET), Industrial University of Ho Chi Minh City. His research interest are optical materials, wireless communication in 5G, energy harvesting, performance of cognitive radio, physical layer security, and NOMA. He can be contacted at email: [email protected]. Nhat-Tien Nguyen received the B.Eng. degree from the Posts and Telecommunications Institute of Technology, he was a Senior Technician at Saigon Postel Corporation from 2003. He received the M.Eng. degree from the Ho Chi Minh City University of Technology (HCMUT) in 2017. He was a Lecturer at Saigon University from 2018, and he is currently pursuing the Ph.D. degree in Communication Technology at the Technical University of Ostrava, the Czech Republic. His research interests include MIMO, NOMA, D2D transmission, energy harvesting, millimeter wave communications, hybrid satellite-terrestrial networks and wireless sensor networks. He can be contacted at email: [email protected]. Duy-Hung Ha received B.S. and M.S. degrees in Electronics and Telecommunications Engineering from Institute of Post and Telecommunication, Vietnam; University of transport and communications, Ha Noi, Vietnam in 2007 and 2014. In 2017, he joined Faculty of Electrical and Electronics Engineering of Ton Duc Thang University, Vietnam as a lecturer. In 2021, he is degrees Ph.D in communication technology at VSB Technical University of Ostrava, Czech Republic. His major interests are cooperative communications and physical-layer security. He can be contacted at email: [email protected]. Miroslav Voznak (M’09-SM’16) received his Ph.D in telecommunications in 2002 from the Faculty of Electrical Engineering and Computer Science at VSB–Technical University of Ostrava, and achieved habilitation in 2009. He was appointed full professor in Electronics and Communications Technologies in 2017. His research interests generally focus on ICT, especially on quality of service and experience, network security, wireless networks, and big data analytics. He has authored and co-authored over one hundred articles in SCI/SCIE journals. According to the Stanford University study released in 2020, he is one of the world’s top 2% of scientists in networking & telecommunications and information & communications technologies. He served as a general chair of the 11th IFIP Wireless and Mobile Networking Conference in 2018 and the 24th IEEE/ACM International Symposium on Distributed Simulation and Real Time Applications in 2020. He participated in six projects funded by the EU in programs managed directly by European Commission. Currently, he is a principal investigator in the research project QUANTUM5 funded by NATO, which focuses on the application of quantum cryptography in 5G campus networks. He can be contacted at email: [email protected].