Enabling Multiple Power Beacons for Uplink of NOMA-Enabled Mobile Edge Computing in Wirelessly Powered IoT

As a promising technique, power beacon provides ability of wireless energy transfer to relaying devices in Internet of Things (IoT) to serve far devices with respect to low latency and high spectrum efficiency manner. Mobile edge computing (MEC) enables smart devices to offload parts of their computation-workloads to the cellular base stations associated with edge servers. This paper introduces a promising multiple access technique, namely non-orthogonal multiple access (NOMA) to provide communication service between the base station associated with MEC and far IoT devices. In this paper, we indicate that the multiple power beacons (PBs) benefits to uplink of NOMA-MEC system with the wireless powered IoT. More antennas equipped at smart device and more PBs exhibit reasonable outage performance for the considered system. The simulation results reveal in two folds: (1) our proposed scheme can simultaneously achieve higher spectrum efficiency and ensure prolong lifetime of IoT devices; (2) the mobility of relay leads to select PB appropriately and hence the suitable scheme is realized as comparing two schemes related to ability of energy harvesting and acceptable outage behavior.


I. INTRODUCTION
Due to capability of connecting heterogeneous devices, the IoT has attracted increased attention [1]. IoT can be implemented with wide range of technologies and applications through device to device (D2D) and cellular wireless communications [2]. Conventional IoT terminals or smart devices are limited in term of computation-resources, and poor resource leads to the degraded quality of experience (e.g., a long computational delay) since the resource-hungry services are required. To overcome such difficulty, mobile edge computing (MEC) allows smart devices to actively offload parts The associate editor coordinating the review of this manuscript and approving it for publication was Tie Qiu . of their computation-workloads to the edge servers associated with cellular base stations [3], [4]. The authors in [5] introduced scheme enabling the IoT device to optimize the offloading policy without three terms including the energy consumption model, knowledge of the MEC model and the computation latency model. Integrating MEC with wireless power transfer is a promising technique in the IoT network introduced in [6]. IoT together with applications provides the better communication quality services for the fifth generation (5G) [7] and beyond 5G (B5G) [8]- [10]. These investigations are developed to satisfy demand in both the academia and the industry in recent years. IoT will play an irreplaceable role and it is benefited from the advantages and the development of the IoT systems. For example, applications of IoT are introduced for 5G and B5G systems [11]- [13]. Meanwhile, two major problems of the IoT need be urgently addressed. Firstly, limitation of the spectrum resources occurs since the widespread deployment of the IoT devices. Secondly, it is a critical problem of power consumption and prolonging the lifetime of the IoT since most of the devices are battery powered constraint. Fortunately, several effective technologies in terms of spectrum sharing and power control have been developed in order to address these problems. For the cellular IoT, NOMA is proposed due to higher spectrum efficiency. NOMA provides an innovative access scheme to accommodate multiple users. These multiple users can be shared on the same frequency (or time) through successive interference cancellation (SIC) technology [14]- [16].

A. RELATED WORK
Regarding implementing wireless power transfer to green networks, the base station provides energy to devices and support to transmit information for uplink communication by using NOMA as recent work [17], [18]. A similar study for a wireless-powered sensor network was conducted in [19]. The authors in [20] studied a NOMA based heterogeneous network to consider the trade-off among harvested energy, sum rate, the energy efficiency and fairness. A cognitive radio-assisted NOMA networks are presented by evaluating optimal resource allocation strategies as in [21]. The machine-to-machine communication benefits from wireless power transfer technique and NOMA scheme. In such network, the machine-type communication device is able to harvest energy in the downlink while the uplink transmitting information to the base station via machine-type communication gateway as in [22], [23]. It is not simultaneous implementation of energy harvesting and information detection since these works studied problems for single antenna nodes which either harvest energy or decode information. In cooperative NOMA systems relying energy harvesting [24]- [26], the cellcentered users harvest energy from the base station based on the wireless received signals. These harvesting users play role as a relay to forward the information to the cell-edge users (far users). Most of works used power splitting based energy harvesting at the relay users. For example, the authors in [30]- [33] derived expressions of outage probability for far users.

B. OUR CONTRIBUTION
However, above works only focus on the outage improvement in relaying networks, even in condition of energy-constrained users which are deployed to forward signal to far users, while neglect the ability of energy harvesting from the beacons [24]- [26]. In other challenging work, secure performance is considered in the situation of IoT using multiple power beacons (PBs) in the presence of a passive eavesdropper, which is very advantageous for energy constrained IoT devices [34]. However, when the harvested energy is applied in the energy-constrained devices in challenging network, i.e. such as NOMA-MEC, is insufficient, the system meets worse performance since it cannot assist the NOMA transmission, i.e., outage performance need be evaluated. Therefore, it is necessary to ensure the data transmission with higher reliability of for wireless powered IoT devices in energy-efficient way.
According to the literature reviews above, though there are lots of work considering both energy harvesting and NOMAenabled MEC network, the research on outage performance for such network can still be further improved. Therefore, considering uplink of NOMA-MEC network under help of multiple PBs, namely a beacon-assisted NOMA-MEC system is proposed in this paper to improve energy shorten existing in IoT applications. On one hand, different from the traditional NOMA network, beacon-assisted NOMA-MEC can achieve low outage probability compared with orthogonal multiple access (OMA). Furthermore, this proposed system can achieve the best trade-off between information and lifetime for energy-limited wireless networks. The contributions of this article are summarized as follows: • We consider multiple PBs and relay scheme to serve NOMA-MEC transmission in main links, where the best PB is selected by the relay. Compared with the OMA scheme and the NOMA-MEC scheme is able to fully utilize the power transfer channels contributed by multiple PBs.
• We derive the closed-form expressions of the outage probability for evaluating ability of wireless power transfer from best power beacon to serve far IoT devices for signal transmission in uplink. Simulation results demonstrate performance gap of two MEC devices in term of outage probability related with higher number of transmit antennas and higher number of beacons.
• This system benefits from multiple antennas architecture, i.e. by increasing the number of antennas and power beacons the outage performance can be improved significantly. Furthermore, simulation results indicated that the outage performance of the proposed scheme is slightly better than that of the OMA-MEC model. The rest of this paper is organized as follows. Section II describes the NOMA-MEC system in two scenarios related to capability of energy harvesting. In Section III, we consider the scenario of energy harvesting which is enabled at relay. Section IV extends our works to the scenario of two nodes are able to harvest energy. Similarly, we analyze the outage performance of OMA-MEC system. We conduct extensive simulations in Section VI, and Section VII concludes the paper.
Notation: Throughout this paper, Pr (.) denotes probability, F Z (.) and f Z (.) symbolize the cumulative distribution function (CDF) and the probability density function (PDF) of a random variable Z , respectively, and K 1 {.} is the first order modified Bessel function of the second kind.

II. SYSTEM MODEL
We consider as illustration in Fig. 1 and Fig. 2 corresponding two cases: (i) only relay harvests wireless energy, (ii) both  the smart camera (denoted as S) and relay R are able harvest energy. In particular, we study a uplink of cooperative NOMA network with one multiple antenna smart camera which intends to communicate with two edge servers (associated with base stations) D 1 , D 2 . In the second scenario of IoT network, the smart camera and the relay are power-constraint devices and they need help of N power beacons (denoted as PB) B 1 , B 2 , . . . , B N . It is assumed that the these PBs are clustered relatively closely together such that they have equivalent distances to the relay. Therefore, the channel gains between the PBs and the relay are independent identically distributed (i.i.d.), as commonly assumed in the related existing work [36]. It is noted that the main parameters are shown in Table 1.
In the first scenario, only power-constraint relay R is able to harvest wireless energy from the group of PBs. This assumption is reasonable for IoT networks which contain equipment (sensors, relays) everywhere. Here, PB selection is adopted as in [34]. 1 In this system model, each node is facilitated with single antenna, except for the S. Due to deep fading, it is assumed that the direct links do not exist between the S and two MEC devices. 2 In Scheme 1, the S communicates with the distant base stations in the uplink with the assistance of the relay under ability of energy harvesting. In Scheme 2, both the smart camera S and the relay R are equipped with small batteries for energy storage due to the size and cost limitations. The camera S sends the superimposed signals x 1 , x 2 dedicated to two MEC devices. The two signals x 1 , x 2 1 Although, the non-linear energy harvester is adopted as in [26]- [29], however multiple beacons allow system a chance to achieve improved performance. In non-linear energy harvester, the amount of harvested energy depends on the saturated threshold at the harvester. We also extend to case of non-linear energy harvester in future. 2 Our work can be easily extended to multiple user scenario or as our future work. are allocated corresponding power allocation factors a 1 , a 2 , respectively.
In the first phase, the received signal at the link S → R is given by where a 1 +a 2 = 1 and without loss of generality, it is assumed that a 1 > a 2 . Based on the decoding principle of NOMA, the relay R decodes signal x 1 by treating the second base station's signal x 2 as noise. Hence, the signal to interference plus noise ratio (SINR) to decode x 1 at R is given by After performing SIC, the SINR to decode x 2 at R is expressed as The decoded and re-encoded symbols are then further processed in the second phase. In particular, R forwards the re-encoded symbols to expected base stations in the uplink. The received signals at D i are given by The SINR to decode x 1 at D 1 is given by The SINR to decode x 1 at D 2 is given by Similarly, SIC is required at the destinations, the SINR to decode x 2 at D 2 is formulated by According to the transmit antenna section strategy, the camera S selects the antenna with the maximum quality of corresponding link to forward the message to the relay. Then, it can be acquired the diversity gain. It is noted that selection of best antenna by the source based on feedback of the CSI of link from the camera S to relay. In particular, to strengthen signal transmission of link S → R link, the antenna index can be selected at the camera as [37] The selected PB with index n * is required to strengthen link from group of PBs to relay as 3 From (8) and (9), the CDF and the PDF related selected channel are given respectively by where (Z = {S k , B n }), and

III. SCHEME 1: ENERGY HARVESTING AT THE RELAY
In the considered system, the relay R harvests energy from PB, and then such harvested energy is reused to transmit signals to far users. To robust wireless power transfer, the best PB in the considered system is selected to improve capability of energy harvesting from PB to the relay R. In addition, we assume that the time switching based energy harvesting technique is applied thanks to its high throughput [38]. It is denoted T as a transmission block time and R uses a duration of αT to harvest energy from the selected PB. Therefore, the energy harvested at the relay R is formulated by [38] where g B n * R 2 is channel power gains of the links from the chosen PB n * at link from group of power beacon to the relay. It is noted that optimizing problem of α is out of the scope of this paper. Under the assumption that the processing energy at R is negligible, the transmit power of R is written as [38] where ξ = 2τ P B α (1−α) .

A. OUTAGE PERFORMANCE ANALYSIS
An outage event at each user occurs since the SINR during the first and second phases less than the target SINR υ i . Due to the difference in their power allocation coefficients, it is pertinent to note that an outage behavior at D 1 is different from an outage behavior at D 2 . As a result, the following subsections present the outage probability at D 1 , D 2 separately.

1) OUTAGE ANALYSIS AT D 1
To consider outage performance of user D 1 , we compute outage event based on ability of signal detection at related devices R and D 1 as below [39] OP SC1 where υ i = 2 2R i − 1 and R i , i = 1, 2 are target rates of user D i . Proposition 1: The closed-form expression of outage probability at D 1 in Scheme 1 is given as Proof: See Appendix A. Remark 1: Although the outage probability expression given in (15) can be readily evaluated through main parameters such as the number of antennas, transmit SNR at source, it is desirable to obtain reasonable outage probabilities for practical implementation. The antenna selection technique benefits to such outage performance, however we do not rely on this to reduce the computational complexity and cost of hardware design. For other confirmation, in the next subsections, we can be seen very tight matching between mathematical expressions results and simulation based results in the entire SNR range.

2) OUTAGE ANALYSIS AT D 2 WITH PERFECT SIC
Different with capability of signal detection at D 1 , SIC is employed at D 2 . Therefore, such outage probability at D 2 depends on how well SIC works to eliminate signal x 1 before detecting signal x 2 . In case of perfect SIC, the outage probability is formulated as Proposition 2: It can be derived expression of outage probability at D 2 in closed-form as

3) OUTAGE ANALYSIS AT D 2 WITH IMPERFECT SIC
When the imperfect SIC occurs, the SINR to decode x 2 at the link S → R is rewritten as The SINR to decode x 2 related to the link R → D 2 is given by As a result, the outage probability at D 2 in imperfect SIC case is rewritten as Proposition 3: The closed-form expression of outage probability in imperfect SIC case at D 2 is computed by Proof: See Appendix C.

B. ASYMPTOTIC ANALYSIS
In case of P S → ∞, the lower bound of outage probability for users D 1 , D 2 (perfect SIC and imperfect SIC) are respectively given as Remark 2: Such asymptotic outage performance of users provides acceptable limitation of NOMA-MEC system. It is predicted that asymptotic expressions of outage probability result in a good matching with exact expressions of outage probability at specific range of SNR. We further verify these expectations in the section of numerical simulation.
Remark 3: From (22), (23) and (24), diversity order of the system under investigation equals zero. Therefore, these asymptotic expressions related outage performance are independent of transmit SNR at source. In particular, at high SNR, the outage performance will meet the outage floors. This observation is versified in the section of numerical simulation.

IV. SCHEME 2: ENERGY HARVESTING AT BOTH THE CAMERA AND THE RELAY
In the process of wireless power transfer, the operation of camera is limited by power source and hence harvested energy enables camera to prolong its lifetime. In this circumstance, the group of PBs still support both the camera and the relay with similar quality due to randomly selection of PB based on corresponding link's quality. This ability is possible as camera located close to the PBs.
The harvested energy at the camera S can written by Under the assumption that the processing energy at S is negligible, the transmit power of S is given by The outage probability at D 1 in Scheme 2 is defined as Proposition 4: The outage probability of D 1 is computed in the closed-form expression as Proof: See Appendix D.

2) OUTAGE ANALYSIS AT D 2 WITH PERFECT SIC
In case of perfect SIC, outage probability at the second MEC D 2 is formulated as VOLUME 8, 2020 Proposition 5: The closed-form expression for D 2 in case of perfect SIC is derived as Proof: See Appendix E.

3) OUTAGE ANALYSIS AT D 2 WITH IMPERFECT SIC
To indicate outage performance of D 2 with imperfect SIC in Scheme 2, we formulate outage probability as Proposition 6: The closed-form expression in imperfect SIC at D 2 is given as (32), shown in the bottom of the next page.
Proof: See Appendix F. Remark 4: These results indicate that outage probability of NOMA-MEC which depends on various parameters. Firstly, fixed power allocation factor a 1 , a 2 are set at the smart camera and they make outage difference among two MEC devices. The optimal outage performance with respect to a 1 , a 2 is hard problem, it will be considered in future work. However, amount of harvested power P B , P S together with the number of transmit antennas at S and the number of power beacons are main reason to make outage behavior change significantly. Such analysis is further verified in numerical result. 4

V. THE BENCHMARK OF OMA-MEC
In this section, OMA-MEC system is considered as a benchmark to highlight advantage of NOMA-MEC. In the first phase, the received signal at link S → R is given by In OMA-MEC mode, the SINR to decode x i at R is given by 4 The problem of energy efficient is reported in [34], in which the timeswitching factor related power beacon can be optimized to maximize by employing the Dinkelbach algorithm with Brent's method, together with the time-consuming exhaustive search approaches.
In the second phase, the received signal at D i is given by The SINR to decode x i at D i is given by In similar way, it can be found outage probability of OMA-MEC in Scheme 1 as In the scenario of both S and R are allowed to harvest energy from group of beacons, the outage event is formulated as Proposition 7: We can compute outage probability of OMA-MEC at D i as  Proof: We omit the proof due to similarity as previous propositions.

VI. SIMULATION RESULTS
In this section, we perform simulations to evaluate the performance of the proposed IoT system. We first reveal the outage performance of the first scheme in which energy harvesting is enabled at only relay R. Then the simulation results are used to provided comparison between two schemes. This paper only presents main metric, i.e. outage probability. We omit the throughput performance metric here since it can be achieved straightforward manner. In these simulations, we set the number of antennas at S is same as the number of beacons K = N = 3 except for specific cases. The other parameters are given, such as target rates R 1 = 0.5 (bps/Hz), R 2 = 2 (bps/Hz), channel gains λ BS = λ BR = 1, λ SR = λ D1 = 10, λ D2 = 5, λ SRip = λ D2ip = 0.01, coefficients related to energy harvesting τ = 0.8, α = 0.6 except for specific cases. Fig. 3 demonstrates the outage performance of the considered system in Scheme 1 versus transmit SNR at S in the uplink NOMA-MEC system. For outage comparison, the outage performance of D 1 is better than that of D 2 which depends on performance of SIC. The main reason is that higher power allocation factor a 1 associated with D 1 . It can be seen clearly that D 2 in perfect SIC provides better outage performance than that in imperfect SIC case. Moreover, asymptotic lines match with analytical curves at high region of transmit SNR at the smart camera S. This is predicted as Remark 3. Such situation confirmed the exactness of our derived asymptotic expressions. In addition, this figure compares two cases (K = 5, 10) of antenna configuration at S. Since S is equipped more antennas, it can be observed that lower outage probability occurs at K = 10. It is also proved that analytical results are matched with numerical results. Fig. 4 depicts similar trends as Fig. 3; however varying transmit SNR at the PB makes the proposed system in OMA with K = 10 meets saturation early than other curves. This can be explained by diversity order equaling zero. Fig. 5 indicates significant impact of power allocation factors on system performance of D 1 , D 2 versus target rates required at MEC devices. It confirms that performance gaps of each device with two cases a 1 = 0.8, a 1 = 0.9 can be seen clearly in entire range of target rates. We set P S /N 0 = 40 (dB), P B /N 0 = 10 (dB). This illustration allows system to adjust factor a 1 to achieve fairness among two MEC devices.
It need be further examined impact of amount of harvested energy on outage performance versus energy efficiency factor τ at S as in Fig. 6. Comparing outage performance of two MEC devices with two cases P S /N 0 = 10 (dB), P S /N 0 = 20 (dB), small gap exists in the base station D 1 and D 2 with perfect SIC. By increasing τ , the outage performance changes slightly. It can be explained that there exists saturated threshold for harvested power at the relay R related to outage performance.
VOLUME 8, 2020  It can be observed the improvement of outage performance of Scheme 2 for two devices by enhance quality of wireless channel as in Fig. 7. The stronger channels of two links, i.e. link the selected PB to S, link the selected PB to relay make influence on outage behavior of D 1 , D 2 . This observation provides the guidelines to locate the group beacon close to both the smart camera and the relay to achieve better performance. Although small amount of harvested energy is bewared, but strong wireless powered channels contribute to enhance outage behavior of two devices. It should be balance between benefits of energy harvesting and ability of signal processing. Fig. 8 compares outage performance of two schemes. Interestingly, although the smart camera S harvests energy to serve for its uplink to MEC, outage performance corresponds to Scheme 2 is still slightly better than that of Scheme 1 once P B /N 0 is greater than 20 (dB). That can be explained by higher power facilitated to PBs benefits to the proposed system in two schemes. Two schemes exhibit the same performance at low region of P B /N 0 and P S /N 0 = 10 (dB). This observation confirms such NOMA-MEC still benefits from  energy harvesting to improve operation of sensors with limited power resource. The distance between the power beacon and sensor nodes is key factor to improve outage performance since energy efficiency is very limited in current technology of circuit [34].

VII. CONCLUSION
In this paper, we proposed a uplink for NOMA-enabled MEC system operating under ability of energy harvesting from the group of PBs. We derive exact closed-form expression of outage probability for each signal at MEC associated with the base stations. In addition, we examined two scenarios of opportunity of energy harvesting from the relay or the source, which was compared in term of outage performance sequentially. It was shown that the proposed system provides NOMA-enabled MEC with better outage performance than OMA-enabled MEC. In addition, the outage improvement can be obtained since more antennas equipped at the camera (sensor) in such IoT system and more PBs are activated. As a future work, optimal user pairing algorithms for NOMAenabled MEC system will be considered under multi-MEC scenario.

PROOF OF PROPOSITION 2
From (10) and (16), ∇ SC1 1 can be expressed by can be computed from result in (16) as From (10) and (11), by exploiting related CDF and PDF, (16), the final result can be obtained as in Proposition 2.
It is the end of the proof.

PROOF OF PROPOSITION 3
From (10) and (20), we can express ψ SC1 (C.1) By exploiting related CDF and PDF, ψ SC1 1 is further computed by From (20), ψ SC1 2 can be rewritten as In similar way, ψ SC1 2 is formulated by (C.4), as shown at the top of the next page The expected result can be obtained by plugging (C.2), (C.3), into (20).
It is the end of the proof.

PROOF OF PROPOSITION 4
With the help of (25), ∂ SC2 1 can be expressed by Plugging (A.2), (D.1), into (25), the final result can be obtained as in Proposition 4. It is the end of the proof.
It is the end of the proof.
It is the end of the proof.