Hybrid NOMA Based MIMO Offloading for Mobile Edge Computing in 6G Networks

Yunus Dursun,Fang Fang,Zhiguo Ding

1 School of Electrical and Electronic Engineering,University of Manchester,Manchester,UK

2 Department of Electrical and Computer Engineering and the Department of Computer Science,Western University,London,Canada

*The corresponding author,email:yunus.dursun@manchester.ac.uk

Abstract:Non-orthogonal multiple access(NOMA),multiple-input multiple-output(MIMO)and mobile edge computing(MEC)are prominent technologies to meet high data rate demand in the sixth generation(6G)communication networks.In this paper,we aim to minimize the transmission delay in the MIMOMEC in order to improve the spectral efficiency,energy efficiency,and data rate of MEC offloading.Dinkelbach transform and generalized singular value decomposition(GSVD)method are used to solve the delay minimization problem.Analytical results are provided to evaluate the performance of the proposed Hybrid-NOMA-MIMO-MEC system.Simulation results reveal that the H-NOMA-MIMO-MEC system can achieve better delay performance and lower energy consumption compared to OMA.

Keywords:NOMA;MEC;MIMO;Generalized singular value decomposition;sixth generation networks(6G);delay minimization

I.INTRODUCTION

Increasing demand for both achieving higher data rate to solve computationally intensive tasks timely and connecting more user equipment(UEs)simultaneously have prompted researchers to develop new technologies in the area of wireless communications.Transmission delay time is a comprehensive metric for satisfying these demands.

Non-orthogonal multiple access(NOMA),multipleinput multiple-output(MIMO)and mobile edge computing(MEC)are promising technologies for minimizing the uplink/downlink transmission delay[1,2].Specifically,NOMA,which hosts more than one user in the same sub-carrier by exploiting power domain,could play a vital role in the next generation communication networks due to its higher spectral efficiency,lower latency,user fairness,and greater connectivity features compared with the traditional orthogonal multiple access(OMA)techniques[3].Motivated by the advantage of high throughput due to array and spatial diversity gains,several studies have shown that MIMO will maintain its importance in 5G and beyond[1].Driven by the increasing applications with computationally intensive tasks,MEC was proposed to reduce the computation time.The main idea behind MEC technology is to bring mini cloud computers to the edge.Therefore,UEs in the cell can enjoy the cloud computing-like facilities by offloading their computationally complex tasks to the MEC server[4].

Existing studies with MEC mainly utilized OMA protocols[5,6].Joint optimization of radio resource and computation resource have been investigated in order to reduce energy consumption with latency constraints for the OMA-based MIMO-MEC system[5].In[7],the weighted sum of energy consumption and round transmission delay for OMA based multi-user MIMO-MEC offloading were minimized by using the semi-definite relaxation(SDR)method.In[8],an inter-user task dependency problem was investigated while minimizing a weighted sum of energy and of-floading delay in the time division multiple access(TDMA)based SISO-MEC systems.In[6],a TDMA based multiple input single output(MISO)-MEC system was integrated with secure wireless power transfer(WPT).

Table 1.Comparison of OMA,NOMA and H-NOMA.

Recently,researchers have demonstrated the superiority of NOMA over OMA in the single-input singleoutput(SISO)-MEC for a delay minimization problem[2].In[9],offloading tasks partition ratio and offloading transmit power of the users were jointly optimized to minimize the offloading delay.In[10],energy consumption minimization problem was studied for a multi-user multi-BS NOMA-MEC network with imperfect channel state information(CSI).In[11],total energy consumption was minimized by optimising the user clustering,computing and communication resource allocation,and transmit power for the NOMAbased SISO-MEC.In[12],a NOMA based secure and energy efficient massive MIMO system was investigated.

Hybrid NOMA(H-NOMA)is a hybrid multiple access concept that combines NOMA and OMA.More specifically,if there are two H-NOMA users in a cluster,the users start uploading/downloading their data concurrently by using NOMA protocol.Once one of the users completes its transmission,the other user switches to OMA protocol to upload/download its remaining task.The advantages and disadvantages of the H-NOMA,comparison with OMA and NOMA,are presented in Table 1.H-NOMA achieves better delay performance compared to pure NOMA and OMA as energy consumption are considered[2].In[13],power allocation,time slot allocation,task assignment and user grouping methods were utilised to minimize energy consumption in the H-NOMA based SISO-MEC system.

In SISO-NOMA,two channels can be compared and their corresponding transmit powers can be allocated to the channels,but it is not as easy for MIMO as it is in SISO.The generalized singular value decomposition(GSVD)method,which simultaneously decomposes two matrices into their singular values,was proposed for MIMO-NOMA uplink and downlink transmissions in[14].

Existing studies on NOMA based MEC were mostly build on SISO transmission[2,11,13].In order to exploit MIMO’s diversity gain and H-NOMA’s superior delay performance[2]with balanced spectral efficiency and system complexity features[15],we integrate H-NOMA,MIMO and MEC technologies by the GSVD technique.To this end,an optimal power allocation problem is formulated.The problem is a non-convex problem.Therefore,some insights are provided to transform the non-convex problem into a suboptimal convex form.The delay minimization problem is divided into two subproblems which are represented by two time-frames:T1andT2.T1represents the total offloading delay during NOMA transmission,andT2is for OMA transmission.In addition,the MIMO channels between UEs and the MECassisted base station are decomposed into SISO channels by using the GSVD and the singular value decomposition(SVD)techniques according to the H-NOMA method.Moreover,we only focus onT2becauseT1is a basic concave problem[2].In other words,T1could be easily solved by numerical methods.Due to the fractional form ofT2,the Dinkelbach method[16]is applied to transformT2into a subtractive form.After the transformation,an iterative closed-form solution forT2is derived by using the Karush-Kuhn-Tucker(KKT)conditions.Finally,delay performance of the OMA-MIMO-MEC and H-NOMA-MIMO-MEC systems are compared.The effect of the antenna number on delay in the H-NOMA-MIMO-MEC system is also investigated.

Figure 1.H-NOMA based MIMO MEC system model.

II.SYSTEM MODEL

We consider a MIMO-NOMA-MEC uplink communication scenario in which one MEC-assisted eNodeB communicates with two UEs,as shown in figure 1.We assume that the base station has M antennas and each UE has K antennas.In this system model,we consider the H-NOMA scheme due to its superior delay minimization performance[2].The objective of the model is to minimize the total offloading time for bothUE1andUE2.We also assume thatUE1is the near user,and it has a higher SINR rate thanUE2.As shown in figure 2,UE1offloads its task duringT1.Concurrently,UE2offloads its task.However,UE2might not complete its task inT1due to its lower SINR.Therefore,UE2needs to continue offloading duringT2to complete its task.Accordingly,the total delay time forUE2can be found byT1+T2.Under the timeinvariant wireless channel condition,the received signal at the base station can be formulated as follows:

Figure 2.A basic concept of H-NOMA.

where y is anM×1 dimensional vector.xi∈C1×Kdenotes information vector created by thei-th user,n∈CM×1denotes a complex additive noise with zero mean andσ2nvariance.Hi∈CM×Krepresents a complex Gaussian channel matrix betweenUEiand the base station.Hican be decomposed into SISO channels by GSVD as follows:

where U is anM×Mmatrix,Viis anM×Munitary matrix and Λi=diag(σi,1,...,σi,K).In addition,we assume that the users have perfect channel state information(CSI).The power of the transmitted signalxi,jis set to be normalized.Therefore,the received signal at the MEC-assisted base station can be expressed as:

In the H-NOMA based system,the achievable maximum data rates are denoted byR1andR2forUE1andUE2,respectively.In comparison to NOMA,these rates in an OMA system,i.e.,orthogonal frequency division multiple access(OFDMA)are given byR3andR4.

whereBis the bandwidth.σ1,jandσ2,jare the generalized singular values;σ3,jandσ4,jare singular values of the strong channel and the weak channels,respectively.The power allocation expressions of the j-th subchannels forUE1andUE2are denoted byPN1,jandPN2,jin NOMA;PO1,jandPO2,jare the power allocation expressions in OMA as illustrated in figure 2.

III.PROBLEM FORMULATION AND SOLUTION

As 6G networks are expected to serve unprecedented number of UEs with different data rate requirements and power constraints,we formulate the transmission delay problem based on the H-NOMA technique in this section.According to H-NOMA,T1andT2correspond to the delay time during NOMA and OMA transmission in(5),respectively.The delay minimization problem can be formulated as

where(5a)is the objective function minimizing total transmission time.Particularly,NOMA and OMA based transmission time expressions are given in(6)and(7),respectively.The inequality constraints in(5b)and(5c)denote the transmit power limits for the users.(5)can be divided into two sub-problems(8)and(9).

where(8)only depends onPN1,jand for this reason(8)is a concave optimization problem as in[3].To solve(8),we use CVX,a package for specifying and solving convex programs[18].Therefore,we assume thatPN1,jandT1are fixed forT2.However,(9)is still a non-convex problem owing to its concave-to-convex fractional expression in(9b).Fortunately,(9b)can be reformulated as a subtractive optimization problem by applying the Dinkelbach method.AsPN1,jis fixed forT2,(9)can be rewritten as follows:

The Dinkelbach transform is applied to(10)as follows:

where q is the Dinkelbach parameter.Thus,(9)is transformed into a convex optimization problem.To obtain the optimal solutions forPN2,jandPO2,j,the Lagrange multipliers method is applied to(11).The Lagrange function of(11)is written as follows:

whereλiare the Lagrange multipliers.The KKT conditions are derived to find the optimal solutions as follows:

The optimal solutions forPN2,jandPO2,jare given in Lemma 1.Algorithm 1 describes the Dinkelbach’s method based closed form solution.

Lemma 1.H-NOMA power allocation policy.

wheremax(a,b)denotes the maximum of a and b.

Proof.Please see Appendix.

Complexity Analysis

The time complexity of the proposed algorithm is analyzed in this subsection.Algorithm 1 consists of two loops:the outer loop is to apply the Dinkelbach algorithm and the inner loop,which is a waterfilling like solution,is to specify the number of power allocated sub-channels(K)and to assign optimal power.The Dinkelbach parameterqis updated in each iteration untilf(q)<Δ.The computational complexity of the Dinkelbach algorithm isO(T),whereO(.)describes the upper bound of the time complexity andTis the number of iterations required for convergence of the Dinkelbach algorithm[19].The required number of operations,at worst,for the inner loop isO(K),whereKis the minimum rank of the near and the far users’channel matrices.Therefore,the proposed algorithm has a complexity ofO(TK).

Figure 3.Delay performance comparison of H-NOMAMIMO-MEC with OMA-MIMO-MEC.

Figure 4.Delay performance of antenna numbers in HNOMA-MIMO-MEC system.

IV.NUMERICAL STUDIES

In this section,we evaluate the performance of the proposed H-NOMA-MIMO-MEC system.In the simulations,we consider that there are two randomly distributed users in the cell and an MEC-assisted base station at the cell centre.We assume that the cell radius isr=125 meters,the carrier frequency isfc=2 GHz,the total bandwidth isB=10 MHz,AWGN spectral density isN0=-174 dBm/Hz and the number of bit needs to be offloaded isN=1 Gbit for each user.

Figure 5.Total energy consumption versus power budget.

Figure 6.Convergence performance of the proposed algorithm in terms of iteration number.

In figure 3,the offloading delay performances of the H-NOMA and OMA based MIMO-MEC systems are demonstrated.The base station and theUEsare equipped with three antennas.The figure clearly demonstrates that the H-NOMA-MIMO-MEC achieves better performance than OMA-MIMO-MEC,particularly at higher power levels.This is because the weak NOMA user suffers from co-channel interference at low SNR.Also,it can be concluded that increasing transmit power has less impact on delay minimization compared with bandwidth.This is one of the key advantages of using NOMA.Figure 3 shows that the H-NOMA-MIMO-MEC improves delay performance by an average of 11% compared to the OMAMIMO-MEC.In figure 4,the impact of antenna numbers on transmission delay is demonstrated.Transmission delay is closely related to the antenna number.As seen from the figure,the proposed H-NOMA based MIMO-MEC achieves better delay performance compared to SISO-MEC.The most striking result from the figure is that having more antennas improve delay performance significantly on the low transmit power region.In figure 5,energy consumption of the HNOMA based MIMO offloading system is compared with OMA.It can be seen that NOMA yields better results for each antenna configuration.Since the power budgets are the same for the UEs in H-NOMA and OMA transmissions and the proposed H-NOMA based system completes offloading earlier than OMA,energy efficiency is improved.figure 6 presents sublinearly convergence of the proposed algorithm versus iteration number.It can be observed in figure 6 that the algorithm significantly converges within 20 iterations for H-NOMA-MIMO-MEC.

V.CONCLUSION

Recent developments in wireless communication have increased the need for spectrum efficiency,energy efficiency,and data rate.This is the first study to combine H-NOMA,MIMO and MEC technologies for delay minimization.In this paper,the H-NOMA-MIMOMEC offloading delay was investigated.Due to the concave-to-convex fractional nature of the problem,the Dinkelbach method was used to eliminate fractional expression.Finally,an iterative closed-form solution was obtained.According to the simulation results,the proposed method improved the delay performance and reduced the total energy consumption of the MIMO-MEC.

ACKNOWLEDGEMENT

This work was supported by Republic of Turkey Ministry of National Education.The authors would like to thank the anonymous reviewers for their valuable comments and suggestions.

APPENDIX

Proof of Lemma 1

Proof.To find the optimal value for,it is necessary to show that there is no more feasible descent for(11)in terms of.Therefore,(13a)is executed as follows:

λ1,jis the vector consisting of the Lagrange multipliers(λ1,1,...,λ1,K)corresponding to(PO2,1,...,PO2,K),respectively.From the complimentary slackness condition in(13c),eitherPO2,jorλ1,jmust be zero.When a MIMO channel is decomposed into decoupled SISO channels,some of these channels may not be feasible for power allocation.Accordingly,we introduce a variable(L)indicating the number of power allocated SISO channels.Hence,we can eliminateλ1,jexpression in(15a)for the weak SISO channels.Therefore,λ3can be written as follows:

It is clear from(15b)thatλ3is positive.Therefore,(15c)can be obtained from(13e).

Furthermore,can be simplified as follows:

Finally,by combining(15b)with(15d),the optimal expression forbecomes

We follow similar steps to those above to find the optimal expression for.(12a)is differentiated with respect toas follows:

λ2,jgoes zero for power allocated sub-channels.Thus,λ4becomes

PN2,jcan be manipulated as follows:

We rewrite(13f)by using(16c)as

We combine(16b)with(16d).Finally,the optimal power allocation expression forPN2,jis as follows:

Therefore,the proof for Lemma 1 is complete.