Secure and Energy-Efficient Offloading and Resource Allocation in a NOMA-Based MEC Network
aa r X i v : . [ ee ss . S Y ] F e b Secure and Energy-Efficient Offloading and ResourceAllocation in a NOMA-Based MEC Network
Qun Wang † , Han Hu ∗ , Haijian Sun ‡ , Rose Qingyang Hu †† Department of Electrical and Computer Engineering, Utah State University, Logan, UT, USA ∗ Jiangsu Key Laboratory of Wireless Communications,Nanjing University of Posts and Telecommunications, Nanjing, China ‡ Department of Computer Science, University of Wisconsin-Whitewater, Whitewater, WI, USAEmails: [email protected], han [email protected], [email protected], [email protected]
Abstract —Energy efficiency and security are two critical issuesfor mobile edge computing (MEC) networks. With stochastictask arrivals, time-varying dynamic environment, and passiveexisting attackers, it is very challenging to offload computationtasks securely and efficiently. In this paper, we study the taskoffloading and resource allocation problem in a non-orthogonalmultiple access (NOMA) assisted MEC network with securityand energy efficiency considerations. To tackle the problem, adynamic secure task offloading and resource allocation algorithmis proposed based on Lyapunov optimization theory. A stochasticnon-convex problem is formulated to jointly optimize the local-CPU frequency and transmit power, aiming at maximizing thenetwork energy efficiency, which is defined as the ratio of thelong-term average secure rate to the long-term average powerconsumption of all users. The formulated problem is decomposedinto the deterministic sub-problems in each time slot. The optimallocal CPU-cycle and the transmit power of each user can be givenin the closed-from. Simulation results evaluate the impacts of dif-ferent parameters on the efficiency metrics and demonstrate thatthe proposed method can achieve better performance comparedwith other benchmark methods in terms of energy efficiency.
Index Terms -Edge computing, physical layer security, Lyapunovoptimization, resource allocation, NOMA.
I. I
NTRODUCTION
The explosive data traffic growth, fast development, andcommercialization of the 5G wireless communication networksimpose great challenges on data security as well as globalenergy consumption [1]. In order to improve energy efficiency(EE), mobile edge computing (MEC) and non-orthogonal mul-tiple access (NOMA) have been envisaged as two promisingtechnologies in 5G and the forthcoming 6G wireless networks.By deploying edge servers with high computational capacitiesclose to end users, the end users can offload partial or allcomputation tasks to the nearby MECs to save power as well asspeed up the computing [2]. Meanwhile, by exploiting super-position coding at the transmitter and successive interferencecancellation (SIC) at the receiver, NOMA brings significantchanges to the multiple access. NOMA allows multiple usersto share the same radio bandwidth in either power domain orcode domain to improve spectral efficiency with a relativelyhigher receiver complexity [3].
The project has been sponsored by the National Science Foundation undergrant NSF EARS-1547312 and CNS-2007995.
Applying NOMA into MEC-enabled networks has recentlyreceived extensive attention due to its performance gain inboth spectrum efficiency and EE [4]- [6]. Most of the existingworks didn’t taking the security issue into account.In fact, dueto the broadcast nature of the wireless link, it could be veryvulnerable for the tasks to be intercepted by the eavesdroppers.The physical layer security (PLS) in the NOMA-assisted MECnetworks has received many research interests [7]. The jointconsideration of PLS in the NOMA assisted MEC network wasstudied in [8]- [10]. In [8], an iterative algorithm was proposedto maximize the minimum anti-eavesdropping ability in a MECnetwork with uplink NOMA. The authors in [9] proposed abisection searching algorithm to minimize the maximum taskcompletion time subject to the worst-case secrecy rate. Insteadof only considering the power consumption or computing rateperformance above, [10] studied the EE maximization problemfor a NOMA enabled MEC network with eavesdroppers.Most of the existing works on NOMA-assisted MEC withexternal eavesdroppers typically focus on the performanceevaluation in the scenarios where either channel conditions orrequired tasks remain constant. Such an assumption makes theanalysis on the computation offloading and resource allocationmore tractable. However, in a dynamic environment, the dy-namic behaviors of the workload arrivals and fading channelsimpact the overall system performance. Thus the system designthat focuses on the short term performance may not work wellfrom the long term perspective. Towards that, a stochastic taskoffloading model and resource allocation strategy should beadopted [11]. In this paper, we integrate PLS and study thelong-term EE performance in a NOMA-enabled MEC network.By incorporating the statistical behaviors of the channel statesand task arrivals, we formulate a stochastic optimization prob-lem to maximize the long-term average EE subject to multipleconstraints including task queue stability, maximum availablepower, and peak CPU-cycle frequency. An energy-efficientoffloading and resource allocation method based on Lyapunovoptimization is proposed. The simulation results validate thesuperior performance of the proposed method in terms of EEin a secure NOMA-assisted MEC network.The rest of the paper is organized as follows. Section IIdescribes the system model. In Section III, the EE maximizationroblem and corresponding alternative solution are presented.Numerical results are provided in Section IV. The paper isconcluded in Section V.II. S
YSTEM M ODEL
UE 2 UE N UE 1MEC server
UE-MEC linkUE-Eve link
Eavesdropper
Fig. 1. System Model.
In Fig. 1, an uplink NOMA communication system is consid-ered, which consists of N user equipments (UEs), one accesspoint (AP) with the MEC server, and one external eavesdropper(Eve) near the AP. All the UEs can offload their computationtasks to the MEC while the external eavesdropper intends tointercept the confidential information. The arrival task of user n at time slot t is denoted as A n ( t ) . Note that the prior statisticalinformation of A n ( t ) is not required and it could be difficult toobtain in the practical systems. We focus on a data-partition-oriented computation task model. A partial offloading scheme isused, i.e., part of the task is processed locally and the remainingpart of the data can be offloaded to the remote server forprocessing. For each UE, local computing and task offloadingcan be executed simultaneously.Assuming that each UE has buffering ability, where thearrived but not yet processed data can be queued for the nexttime slot. Let Q n ( t ) be the queue backlog of UE n , and itsevolution equation can be expressed as Q n ( t + 1) = max { Q n ( t ) − R totn ( t ) τ , } + A n ( t ) , (1)where R totn ( t ) = R offn ( t ) + R locn ( t ) is the total computingrate of UE n at time slot t , R offn ( t ) and R locn ( t ) are secureoffloading rate and local task processing rate, respectively. τ istime duration of each slot. A. Local Computing Model
Let f n ( t ) denote the local CPU-cycle frequency of UE n ,which cannot exceed its maximum value f max . Let C n be thecomputation intensity (in CPU cycles per bit). Thus, the localtask processing rate can be expressed as R locn ( t ) = f n ( t ) /C n .We use the widely adopted model P locn ( t ) = κ n f n ( t ) tocalculate the local computing power consumption of UE n ,where κ n is the energy coefficient and its value depends on thechip architecture [12]. B. Task Offloading Model
The independent and identically distributed (i.i.d) frequency-flat block fading channel model is adopted, i.e., the channelremains static within each time slot but varies across different time slots. The small-scale fading coefficients from UE n to theMEC server and to the Eve are denoted as H b,n ( t ) and H e,n ( t ) ,respectively. Both are assumed to be exponential distributedwith unit mean [13]. Thus, the channel power gain from UE n to the MEC is given as h i,n ( t ) = H i,n ( t ) g ( d /d i,n ) θ , i ∈ { b, e } , where g is the path-loss constant, θ is the path-loss exponent, d is the reference distance, and d i,n is thedistance from UE n to receiver. Furthermore, to improve thespectrum efficiency, NOMA is applied on the uplink access foroffloading. We assume that h b, ≤ h b, ≤ · · · ≤ h b,N and h e, ≤ h e, ≤ · · · ≤ h e,N . Using SIC at the receiver side, theachievable secure offloading rate at UE n can be given by R offn ( t ) = [ B log (1 + γ b,n ) − B log (1 + γ e,n )] + , (2)where B is the bandwidth allocated to each UE, γ b,n = p n ( t ) h b,n ( t ) P n − i =1 p i ( t ) h b,i ( t )+ σ b,n and γ e,n = p n ( t ) h e,n ( t ) P n − i =1 p i h e,i ( t )+ σ e,n are theSINRs received by the MEC server and the Eve respectively. p n ( t ) is the transmit power of UE n , σ b,n and σ e,n are the back-ground noise variances at the MEC and the Eve respectively. [ x ] + = max( x, . The power consumption for offloading canbe expressed as P on ( t ) = ζp n ( t ) + p r , where ζ is the amplifiercoefficient and p r is the constant circuit power consumption.III. D YNAMIC T ASK O FFLOADING AND R ESOURCE A LLOCATION
A. Problem Formulation
EE is defined as the ratio of the number of long term totalcomputed bits achieved by all the UEs to the total energyconsumption [14], η ( t ) = lim T →∞ T E [ P Tt =1 R tot ( t ) τ ]lim T →∞ T E [ P Tt =1 P tot ( t ) τ ] = R tot τP tot τ , (3)where R tot ( t ) = P Nn =1 R totn ( t ) and P tot ( t ) = P Nn =1 P offn ( t ) + P locn ( t ) are the total achievable rateand consumed power by all the users at t .This work aims to maximize the long-term average EE forall the UEs under the constraints of resource limitations whileguaranteeing the average queuing length stability. Therefore,the problem is formulated as P : max f n ( t ) ,p n ( t ) ηs.t. P totn ( t ) ≤ P max , (4a) lim T →∞ T E [ | Q n ( t ) | ] = 0 , (4b) f n ( t ) ≤ f max , (4c) ≤ p n ( t ) , (4d)where Q n ( t ) is the average queue length of UE n . Theconstraint (4a) indicates that the total power consumed by UEat time slot t should not exceed the maximum allowable power P max . (4b) requires the task buffers to be mean rate stable,which also ensures that all the arrived computation tasks canbe processed within a finite delay. (4c) is the range of localcomputing frequency, and (4d) denotes the transmit power ofeach UE should not be negative. lgorithm 1 Dynamic Resource Allocation Algorithm
1: At the beginning of the t th time slot, obtain { Q n ( t ) } , { A n ( t ) } .2: Determine f ( t ) and p ( t ) by solving P : max f n ( t ) ,p n ( t ) N X n =1 { Q n ( t )( R totn ( t ) τ − A n ( t )) } + V N X n =1 [ R totn ( t ) τ − η ∗ ( t ) P totn ( t ) τ ] s.t. (4 a ) , (4 c ) , (4 d )
3: Update { Q n ( t ) } and set t = t + 1 . Go back to step 1. B. Problem Transformation Using Lyapunov Optimization
The problem P is a non-convex problem, which is difficultto be solved due the fractional structure of the objective func-tion and the long term queue constraint (4b). By introducing anew parameter η ∗ ( t ) = P t − i =0 R tot ( i ) τ P t − i =0 P tot ( i ) τ [14], the problem can betransformed to P , which can be solved in an alternating way. P : max f n ( t ) ,p n ( t ) R tot ( t ) τ − η ∗ ( t ) P tot ( t ) τs.t. (4 a ) − (4 d ) . Note that η ∗ ( t ) is a parameter that depends on the resourceallocation strategy before t -th time block [14]. In the following,the Lyapunov optimization is introduced to tackle the taskqueue stability constraint.To stabilize the task queues, the quadratic Lyapunov functionis first defined as L ( Q ( t )) ∆ = P Nn =1 Q n ( t ) [15]. Next, the one-step conditional Lyapunov drift function is introduced to pushthe quadratic Lyapunov function towards a bounded level. ∆( Q ( t )) ∆ = E [ L ( Q ( t + 1)) − L ( Q ( t )) | Q ( t )] . (6)By incorporating queue stability, the Lyapunov drift-plus-penalty function is defined as ∆ V ( Q ( t )) = − ∆( Q ( t )) + V [ R tot ( t ) τ − η ∗ ( t ) P tot ( t ) τ ] , (7)where V is a control parameter to control the tradeoff betweenthe queue length and system EE. The minus sign is used tomaximize EE and to minimize the queue length bound. For anarbitrary feasible resource allocation decision that is applicablein all the time slots, the drift-plus-penalty function ∆ V ( Q ( t )) satisfies ∆ V ( Q ( t )) ≥ − C + N X n =1 E { Q n ( t )( R totn ( t ) τ − A n ( t )) } + V N X n =1 [ R totn ( t ) τ − η ∗ ( t ) P totn ( t ) τ ] , (8)where C = U P u =1 ( R max n τ + A max n ) , R max n and A max n are themaximum achievable computing rate and the maximum arrivalworkload, respectively.Thus, P is converted to a series of per-time-slot deter-ministic optimization problem P , which needs to be solvedat each time slot and is given as in Algorithm 1 . In P , f ( t ) and p ( t ) can be decoupled with each other in both the objective function and the constraints. Thus, the problem P can be decomposed into two sub-problems, namely the optimalCPU-cycle frequency scheduling sub-problem and the optimaltransmit power allocation sub-problem, which can be solvedalternately in the following. Optimal CPU-Cycle Frequencies Scheduling:
The optimalCPU-cycle frequencies f ( t ) can be obtained by P . : max ≤ f n ( t ) ≤ f max N X n =1 ( Q n ( t ) + V )( R offn ( t ) + f n ( t ) /C n ) − V η ∗ ( t )( κ n f n ( t ) + p r + ζp n ( t )) s.t. κ n f n ( t ) ≤ P max − P offn . (9)Since the objective function of P . and the constraints areconvex with respect to f n ( t ) , the optimal f n ( t ) can be givenas f ∗ n = "s ( V + Q n ( t ))3 V ηκ n C n f max , (10)where f max = min { f max , p ( P max n − ζp n − p r ) /κ n } is theupper bound of the frequency. Optimal Transmit Power Allocation:
For the transmissionpower allocation optimization, the problem P is transformedinto P . : max p n ( t ) N X n =1 B ln 2( Q n ( t ) + V )[ln( n X i =1 p i ( t ) h b,i + σ b,n ) − ln( n − X i =1 p i ( t ) h b,i + σ b,n ) − ln( n X i =1 p i h e,i + σ e,n )+ ln( n − X i =1 p i h e,i + σ e,n ) + f n B ln 2 C n ] − V η ∗ ( t )( ζp n + p r + κ n f n ) s.t. ≤ p n ( t ) ≤ ( P max − p r − κ n f n ) /ζ. (11)The minus logarithmic terms make the objective function notconvex, which is addressed by Lemma 1 introduced in thefollowing. Lemma 1 : By introducing the function φ ( y ) = − yx +ln y +1 , ∀ x > , one has − ln x = max y> φ ( y ) . (12)The optimal solution can be achieved at y = 1 /x . The upperbound can be given by using Lemma 1 as φ ( y ) [16]. By setting y b,n = n − P i =1 p i ( t ) h b,i + σ b,n and y e,n = n P i =1 p i ( t ) h e,i + σ e,n ,one has P . : max p n ( t ) ,y b,n ,y e,n N X n =1 B ln 2( Q n ( t ) + V )[ln( n X i =1 p i ( t ) h b,i + σ b,n ) + φ b,n ( y b,n ) + φ e,n ( y e,n ) + ln( n − X i =1 p i ( t ) h e,i + σ e,n )+ f n B ln 2 C n ] − V η ∗ ( t )( ζp n ( t ) + p r + κ n f n ) − Q n ( t ) A n ( t ) s.t. ≤ p n ( t ) ≤ ( P max − p r − κ n f n ) /ζ, (13)here φ b,n ( y b,n ) = − y b,n ( n − P i =1 p i ( t ) h b,i + σ b,n ) + ln y b,n + 1 ,and φ e,n ( y e,n ) = − y e,n ( n P i =1 p i ( t ) h e,i + σ e,n ) + ln y e,n + 1 . Theproblem P . is a convex problem with respect to both p n ( t ) and y b,n , y e,n . It can be solved by using a standard convex opti-mization tool. After we obtain p ∗ n ( t ) , the values of y ∗ b,n and y ∗ e,n can be respectively given by y ∗ b,n = ( n − P i =1 p ∗ i ( t ) h b,i + σ b,n ) − and y ∗ e,n = ( n P i =1 p ∗ i ( t ) h e,i + σ e,n ) − . By alternately updating p n ( t ) and y b,n , y e,n , the optimal solutions of P . can beachieved at convergence. Remark 1:
To obtain fundamental and insightful understand-ing of the offloading power allocation for a multi-user NOMAassisted secure MEC system, we consider a special case withtwo UEs [17]. The problem with respect to p n is given as P . : max p ( t ) ,p ( t ) B ln 2( V + Q ( t ))[ln( p ( t ) h b, + p ( t ) h b, + σ b, ) − ln( p ( t ) h b, + σ b, ) − y b ( p ( t ) h b, + σ b, )+ ln y b + 1 + ln( p ( t ) h e, + σ e, ) + f C B ln 2 ]+ B ln 2( V + Q ( t ))[ln( σ b, + p ( t ) h b, ) − ln σ b, − y e ( σ e, + p ( t ) h e, ) + ln y e + 1 + ln σ e, + f C B ln 2 ] − V η ( ζ ( p ( t ) + p ( t )) + 2 p r + κ n ( f n ) s.t. ≤ p n ( t ) ≤ ( P max − p r − κ n f n ) /ζ. (14) P . is a convex problem with respect to p ( t ) and p ( t ) , andthe optimal solutions are given as p ∗ ( t ) = − b ± p b − b , (15)and p ∗ ( t )= 1( V ηζB ln 2( V + Q ( t )) + y e h e, ) − p h b, h b, − σ b, h b, , (16)where a = V ηζB ln 2 + ( V + Q ( t ))( y b h b, + y e h e, ) +( V + Q ( t )) y e h e, − ( V + Q ( t )) h b, ( V ηζB ln 2( V + Q t )) + y e h e, ) h b, , b =( σ b, /h b, + σ e, /h e, − ( V + Q ( t )) a − ( V + Q ( t )) a ) , and b = σ e, σ b, h e, h b, − ( V + Q ( t )) a σ b, /h b, − ( V + Q ( t )) a σ e, /h e, .IV. S IMULATION R ESULTS
In this section, simulation results are provided to evaluatethe proposed algorithm. The simulation settings are based onthe works in [12], [17]. We consider the configuration with 2UEs, which can be readily extended to a more general case.The system bandwidth for computation offloading is set as B = 1 MHz, the time slot duration is τ = 1 sec, path-lossexponent is θ = 4 , the noise variance is σ i,j = − dBm,where i ∈ { b, e } , j ∈ { , } . The size of the arrival workload A n ( t ) is uniformly distributed within [1 , × bits [18].Other parameter settings include the reference distance d = 1 m, g = − dB, d b, = 80 m, d b, = 40 m, d e, = 120 m, d e, = 80 m. κ n = 10 − , P max = 2 W, f max = 2 . GHz, C n = 737 . cycles/bit, the amplifier coefficient ζ = 1 ,and the control parameter V = 10 . The numerical results areobtained by averaging over random channel realizations.We consider two more cases as the benchmark schemes tocompare with our proposed algorithm. In the first benchmarkscheme, marked as ”Full offloading”, all the tasks are offloadedto the MEC server and there is no local computation at all. Thesecond benchmark [17] is marked as ”Eve fully decode”, inwhich the Eve can correctly decode other users’ information.This provides a worst-case scenario for comparison.
50 100 150 200 250 300 350 400 450 500
Time slot E n e r gy e ff i c i e n c y Proposed designFull offloadingEve fully decode
Fig. 2. System energy efficiency.
The performance of the system EE vs time is presented inFig. 2. We can see that the proposed method can achieve thehighest system EE compared with the other two benchmarkschemes. Furthermore, owing to the flexibility of having bothoffloading and local computing in the proposed scheme andin the “Eve fully decode” scheme, the system can decide notto offload if the eavesdropper has a better channel on theoffloading link while it can decide to offload if the link issecure enough. Therefore, these two schemes have a higherEE performance than the “Full offloading” scheme, which hasto offload even when the links are insecure. The system EEstabilizes for all the three schemes after time slots.
Average arrive task (bits) E n e r gy e ff i c i e n c y Proposed designFull offloadingEve fully decode
Fig. 3. System energy efficiency v.s. Average arrival task length.
The system EE versus the average arrival task length ispresented in Fig. 3. The proposed method achieves the highestEE. For all the three schemes, EE decrease with the increaseof the arrival task length because a higher workload forces thesystem to increase the computing rate to maintain the low queueevel. This in turn decreases the system EE. Furthermore, wenotice that the performance gap between the ”Full offloading”scheme and other two schemes goes up with the increase ofthe task length. This demonstrates that local computing is moreenergy efficient and secure for processing the computation taskswhen the task size goes up.
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Eavesdropper relative distance (m) E n e r gy e ff i c i e n c y Proposed designFull offloadingEve fully decode
Fig. 4. System energy efficiency v.s. eavesdropper relative distance.
Fig. 4 shows the system EE versus the eavesdropper loca-tion. Here the eavesdropper relative distance is defined as thedistance between the eavesdropper and the UE. The proposeddesign achieves the best performance among all the schemes.The system EE of all the schemes goes up as the eavesdropperrelative distance increases since a larger distance leads to aworse intercepting channel at the eavesdropper. Furthermore,the performance gap between the “Full offloading” scheme andthe other two schemes decreases quickly with the increase ofthe relative distance. This is because the secure offloading rateincreases quickly when the eavesdropper moves away.
Maximum available power (W) E n e r gy e ff i c i e n c y Proposed designFull offloadingEve fully decode
Fig. 5. System energy efficiency v.s. maximum available power P max . The relationship between EE and the maximum availablepower is illustrated in Fig. 5. It is observed that EE increaseswith available power and gradually converges to a constantvalue. This is because that when the available power is limited,the higher computing rate and corresponding optimal EE cannotbe achieved. With the power increase, EE of all the schemeskeeps increasing and only stops when it achieves the highestlevel. After the optimal tradeoff has been reached, even there ismore power available in the system, all the schemes maintainat the highest level without consuming any more power. V. C
ONCLUSION
This paper aims to design a secure and energy efficientcomputation offloading scheme in a NOMA enabled MECnetwork with the presence of a malicious eavesdropper. Inorder to achieve a long term performance gain by consideringdynamic task arrivals and fading channels, we proposed asecure task offloading and computation resource allocationscheme that aims to maximize the long-term average EE andused Lyapunov optimization framework to solve the problem.Numerical results validated the advantages of the proposeddesign via comparisons with two other benchmark schemes.R
EFERENCES[1] H. Sun, Z. Zhang, R. Q. Hu, and Y. Qian, “Wearable communicationsin 5G: challenges and enabling technologies,”
IEEE Veh. Technol. Mag. ,vol. 13, no. 3, pp. 100-109, Sep. 2018.[2] H. Hu, P. Zong, H. Wang, and H. Zhu, “Performance analysis forD2D-enabled cellular networks with mobile edge computing,”
Proc.WCSP ,2019, pp. 1-6.[3] Z. Ding, J. Xu, O. A. Dobre, and H. V. Poor, “Joint power and timeallocation for NOMA–MEC offloading,”
IEEE Trans. Veh. Technol. , vol.68, no. 6, pp. 6207-6211, June 2019.[4] Y. Pan, M. Chen, Z. Yang, N. Huang, and M. Shikh-Bahaei, ”Energy-efficient NOMA-based mobile edge computing offloading,”
IEEE Com-mun. Lett. , vol. 23, no. 2, pp. 310-313, Feb. 2019.[5] A. Kiani and N. Ansari, ”Edge computing aware NOMA for 5G net-works,”
IEEE IoT J. , vol. 5, no. 2, pp. 1299-1306, April 2018.[6] Z. Yang, J. Hou, and M. Shikh-Bahaei, “Energy efficient resourceallocation for mobile-edge computation networks with NOMA,”
Proc.GCWkshps , 2018, pp. 1-7.[7] H. Sun, Q. Wang, X. Ma, Y. Xu, and R. Q. Hu, ”Towards green mobileedge computing offloading systems with security enhancement”. [Online],Available: https://arxiv.org/abs/2004.05279.[8] W. Wu, X. Wang, F. Zhou, K. Wong, C. Li, and B. Wang, “Resourceallocation for enhancing offloading security in NOMA-enabled MECnetworks,”
IEEE Systems J. , July 2020.[9] X. Wang, W. Wu, B. Lyu, and H. Wang, ”Delay minimization for secureNOMA mobile-edge computing,”
Proc.ICCT , 2019, pp. 1529-1534.[10] H. Lin, Y. Cao, Y. Zhong, and P. Liu, “Secure computation efficiencymaximization in NOMA-enabled mobile edge computing networks,”
IEEE Access , vol. 7, pp. 87504-87512, 2019.[11] N. Nouri, A. Entezari, J. Abouei, M. Jaseemuddin, and A. Anpalagan,”Dynamic power–latency tradeoff for mobile edge computation offloadingin NOMA-based networks,”
IEEE IoT J. , vol. 7, no. 4, pp. 2763-2776,Apr. 2020.[12] Q. Wang, L. T. Tan, R. Q. Hu, and Y. Qian, “Hierarchical energy efficientmobile edge computing in IoT networks,”
IEEE IoT J. , early access,2020.[13] Y. Mao, J. Zhang, S. H. Song, and K. B. Letaief “Stochastic jointradio and computational resource management for multi-user mobile-edgecomputing systems,”
IEEE Trans. Wireless Commun. , vol. 16, no. 9, pp.5994-6009, Sept. 2017.[14] S. Mao, S. Leng, S. Maharjan, and Y. Zhang, “Energy efficiency anddelay tradeoff for wireless powered mobile-edge computing systems withmulti-access schemes,”
IEEE Trans. Wireless Commun. , vol. 19, no. 3,pp. 1855-1867, Mar. 2020.[15] M. J. Neely, “Stochastic network optimization with application to com-munication and queueing systems,” Morgan & Calypool, 2010.[16] Q. Li, M. Hong, H. Wai, Y. Liu, W. Ma, and Z. Luo, “Transmit solutionsfor MIMO wiretap channels using alternating optimization,”
IEEE J.Select. Areas in Commun. , vol. 31, no. 9, pp. 1714-1727, Sep. 2013.[17] W. Wu, F. Zhou, R. Q. Hu, and B. Wang, “Energy-efficient resourceallocation for secure NOMA-enabled mobile edge computing networks,”
IEEE Trans. Commun. , vol. 68, no. 1, pp. 493-505, Jan. 2020.[18] Y. Deng, Z. Chen, X. Yao, S. Hassan, and A. M. A. Ibrahim, “Paralleloffloading in green and sustainable mobile edge computing for delay-constrained IoT system,”