Abstract
In this paper, a nonorthogonal multiple access (NOMA)based mobile edge computing (MEC) system is proposed, where paired users (the mth user and the nth user) offload tasks to the MEC server under imperfect channel state information (ipCSI) condition. To evaluate the effect on performance under ipCSI condition in NOMAMEC system, this study derives new exact and asymptotic expressions of the offloading outage probability for two users under ipCSI and perfect channel state information (pCSI) conditions. On the basis of the theoretical derivation, the diversity orders of the nth user under ipCSI and pCSI conditions are zero and n, respectively, while those for the distant user are all zeros. In addition, we also investigate the system throughput and energy efficiency of NOMAMEC in delaylimited transmission. Numerical results show that (1) the offloading outage behaviors of NOMAMEC are better than those of time division multiple address (TDMA), (2) the offloading outage performance of paired users under ipCSI is worse than that under pCSI, and (3) the NOMAMEC system achieves higher throughput and energy efficiency than does the TDMAMEC system.
Introduction
Future wireless communication will face the challenges of network requirements, such as highdensity users, high speed, and ultrareliable and low latency communications (URLLC). The latency of URLLC is as low as 1 ms, and the reliability is as high as 99.999%, which can ensure missioncritical communications. In the future 6th generation networks, URLLC will provide powerful guarantee for emerging applications that have strict requirements on latency and reliability [1]. Traditional orthogonal multiple access (OMA) divides physical resources into orthogonal resource blocks in time/frequency/code domains, which limits the number of accessing users. To meet the high requirements of communication networks, highly efficient multiple access technologies are required to improve the system capacity and spectrum utilization under limited spectrum resources. Nonorthogonal multiple access (NOMA)^{Footnote 1} has become a popular research topic in communication systems [3, 4] and has been discussed in the 6th generation mobile communication system for largescale access. NOMA adopts superposition coding to realize the transmission of multiple signals in the same time/frequency/code domains; at the receiver, the information required is extracted by the successive interference cancelation (SIC) scheme to improve the utilization of spectrum resources.
The uplink and downlink communications in NOMA system have been studied by many treatises. For downlink communications, the authors in [5] conducted a detailed study on the performance of NOMA with the perfect channel state information (pCSI) condition by analyzing the outage probability. Furthermore, the ergodic rate of NOMA with pCSI was optimized in [6], through which the authors obtained a closedform globally optimal solution. Considering the low latency in combined with high reliability is a challenging task, the performance of NOMA for URLLC was analyzed in [7], and the results showed that NOMA has reduced the physical layer latency and improved the reliability of supporting the timecritical applications obviously. To draw more conclusions, the authors in [2] proposed a unified framework of NOMA and derived the exact expressions of outage probability as well as the system throughput in delaylimited mode. To study paired users, the authors in [8] developed the optimal and suboptimal schemes. For uplink communications, the performance with pCSI of the NOMA system was characterized by outage probability and achievable sum rate, which is concerned with the power backoff step [9]. To further analyze the performance of uplink NOMA, the authors provide the expressions of effective capacity in [10] and studied the performance of two users under quality of service (QoS) delay constraints. In [11], the authors discussed external and internal eavesdropping scenarios and derived expressions of secrecy outage probability and throughput with pCSI. The impact of pCSI on NOMA systems was investigated carefully in the above researches, while the imperfect channel state information (ipCSI) should be discussed, which is suitable to the practical NOMA scenarios. Based on these, the authors derived a closedform approximation of the outage probability for users and the high signaltonoise ratio (SNR) expressions in downlink NOMA with ipCSI in [12]. To prevent the interception of information between base station and receiver, the authors of [13] studied the secrecy outage probability and average secrecy capacity under ipCSI condition. The influence of ipCSI on the security performance of system could be seen when their is the existence of multiple eavesdropping channels.
URLLC is an important application scenario of the 5th generation networks, with new features of high reliability, low latency, and high availability. In [14], the authors proposed a crosslayer optimization framework to ensure that the wireless access network has ultrahigh reliability and ultralow delay. In order to focus on local communication scenarios, the authors discussed the delay and packet loss of URLLC, as well as the network availability that supports the QoS of users [15]. As cloud capabilities tend toward the network edge, mobile edge computing (MEC) has become a new trend in mitigating the terminal computing abilities. MEC is considered as an effective solution for URLLC, which is capable of reducing the delay of computationally intensive tasks by invoking great computing cells within a short distance [16]. Given that its computing ability is near that of mobile devices and ultralow latency is its greatest advantage, MEC is widely regarded as the key technology of the next Internet generation [17]. Intelligent applications and networks are deeply integrated based on MEC and Internet of Things to achieve the corresponding requirements of users. The MEC server can be distributed at the edge of networks and perform computationintensive and delaycritical tasks from mobile devices [18, 19]. In view of the ultralow latency characteristic of MEC, the authors evaluated its actual delay and throughput performance in cellular networks and found that MEC reduces the delay of downlink communication [20]. To improve the efficiency of offloading tasks, the authors of [21] proposed an energysaving offloading strategy that the computational offloading problem of MEC is transformed into a system cost minimization considering the completion time and energy.
Combining MEC and NOMA is an effective method to utilize computing capacities and improve energy efficiency. The authors in [22] discussed the effect of NOMA on delay and energy efficiency of offloading tasks in MEC, where both uplink and downlink NOMA are taken into consideration. In [23], the authors proposed a NOMAbased computational offloading scheme to reduce the task execution time for users. A distributed algorithm was also proposed to optimize users’ transmission time in [24]. The results showed that NOMAbased MEC has more advantages in delay than traditional frequency division multiple accessassisted MEC. In order to reduce the energy consumption of offloading tasks, the authors developed an optimization framework based on NOMA to optimize communication resource allocation and transmission power [25]. In [26], the authors studied energy consumption, where NOMAbased MEC offload scheduling can reduce the system energy consumption compared with OMA. Moreover, the authors in [27] minimized the offloading delay and analyzed the convergence speed.
This treatise focuses on the combination of MEC and NOMA technology under the ipCSI condition in actual scenarios. Based on [28], the NOMAassisted MEC network is considered where all users transmit the tasks to the MEC server through uplink transmission. The researches in [29, 30] illustrate the advantages of combining NOMA with MEC. However, NOMAMEC is still in its infancy under ipCSI condition. In addition, NOMA has better outage performance than OMA. There are many OMA schemes this paper focuses on comparing NOMA and time division multiple address (TDMA). These are the motivations of this paper. The contributions of this work are summarized as follows:

1)
We study the outage performance under two conditions in NOMAMEC. The NOMA framework studied is applied to the MEC scenario, and the closedform expressions of the offloading outage probability for paired users (the mth user and the nth user) under pCSI and ipCSI conditions through setting the target transmission rate v_{n} and v_{m} are derived. In order to get more conclusions, we also obtain the expressions of the asymptotic offloading outage probability at high SNRs and provide the diversity orders of user. Additionally, we obtain the diversity orders of the both two users are zeros under ipCSI condition. The diversity order of the nth user under pCSI is n, while that of the mth user is zero.

2)
We evaluate theoretical results of system performance by simulation, which shows that the offloading outage probability under ipCSI is larger than that under pCSI. We further analyze the impact of changing channel estimation errors on system performance. With the increasing of channel estimation errors, the offloading outage behaviors for users are becoming more worse. In addition, when the offloading tasks are reduced or the offloading time is increased, the offloading outage probability for the users will be decreased.

3)
We study the throughput and energy efficiency for two users in delaylimited transmission mode of NOMAMEC system and derive the corresponding expressions. We find that NOMAMEC has higher system throughput and energy efficiency than TDMAMEC. In addition, the throughput and energy efficiency under ipCSI are lower than those under pCSI, while the system throughput and energy efficiency will decrease as the channel estimation errors increase.
System model
Considering NOMAbased MEC communication scenario, M users offload tasks to a single MEC server illustrated in Fig. 1. Assume that each node is a single antenna device and operates in half duplex mode. All communication links in network are subject to Rayleigh fading and disturbed by additive white Gaussian noise (AWGN). \({{\widehat h}_{i}} \sim {\mathcal {C}}{\mathcal {N}}\left ({0,{\widehat {\Omega _{i}}}} \right)\) denote the channel coefficients of links between the user and the MEC server, where i∈{1,2,⋯,M}. \({\widehat {\Omega _{i}}}{\mathrm { = }}{d_{i}}^{ \alpha }\), where d_{i} represents the distance between the user and the server, and α is the path loss exponent. Due to channel estimation errors, it is difficult to obtain the pCSI of channels for NOMAMEC system in practical communication scenarios. To evaluate the influence of ipCSI in NOMAMEC system, the channel coefficient is modeled as \({{\widehat h}_{i}} = {h_{i}} + \varpi {e_{i}}\), where ϖ∈(0,1),h_{i} represents the channel gain under the pCSI condition. ϖ=0 denotes that the system has ability to obtain the pCSI, and ϖ=1 denotes that the system cannot obtain the pCSI and will suffer from the channel estimation error \({e_{i}} \sim {\mathcal {C}}{\mathcal {N}}\left ({0, {{\sigma }_{e_{i}}^{2}}} \right)\). Assuming that h_{i} is statistically independent of \({e_{i}}, {\gamma _{i}} = {{\sigma }_{e_{i}}^{2}} \bigg / {{\widehat {\Omega _{i}}}}\) represents the relative channel estimation error and has \({{\sigma }_{e_{i}}^{2}}{\mathrm { = }}{\gamma _{i}}{d_{i}}^{ \alpha }\).
In this paper, two users are selected from M users, i.e., the nth and mth users for nonorthogonal transmission, where a pair of users simultaneously offload tasks to the MEC server. The channel gains between users and the MEC server are sorted as \({{\widehat h}_{m}^{2}} \le {{\widehat h}_{n}^{2}}\), where the nth and mth users have similar channel estimation errors (i.e., h_{m}^{2}≤h_{n}^{2}). On the basis of the principle of NOMA, the received expression of offloading tasks at MEC server is given by:
where x_{j} denotes the offloading task of the jth user, j∈{m,n}. \({n_{\text {MEC}}}\sim {\mathcal {C}}{\mathcal {N}}\left ({0,\sigma _{\text {MEC}}^{2}} \right)\) represents the AWGN at the MEC server. The transmission power of the jth user is denoted as P_{j}, i.e., P_{j}=a_{j}P and P is the total power of the two users. To guarantee better fairness between the users, assume that a_{m}>a_{n} with a_{m}+a_{n}=1. Note that optimal power allocation coefficients [9] can further improve the performance in this system; however, it is beyond the scope of this paper. The mth user has an exclusive time slot in TDMA when offloading the tasks, while the nth user will also enter the slot to complete its offloading tasks in NOMAMEC. The nth user does not need additional time slot, which is an advantage of NOMAMEC compared with TDMAMEC, thus reducing the offloading delay of the system.
According to the principle of uplink NOMA, the MEC server first decodes the task x_{m} with large power allocation coefficient by treating the task x_{n} with small power allocation coefficient as noise and then subtracts this component. After carrying out SIC procedure, the task x_{n} with small power coefficient can be detected. Hence, the signaltointerferenceplusnoise ratios (SINRs) for the MEC server to decode x_{m} and x_{n} are given by:
and
respectively, where \(\rho \buildrel \Delta \over =\frac {P}{{\sigma _{\text {MEC}}^{2}}}\) is the transmit SNR, \({\theta _{j}}{\mathrm { = }}\sigma _{{e_{j}}}^{2}{a_{j}}\rho \).
Assuming that the ith user has N_{i}bits tasks and offloads these to the MEC server, where the time required to execute the tasks is \({T_{\text {MEC}}}{\mathrm { = }}\frac {{2NC}}{{{f_{\text {MEC}}}}}\), N represents the total tasks; C is the number of central processing unit (CPU) cycles demanding for computing one input bit, and f_{MEC} is the CPU frequency at the MEC server.
Performance evaluation
In this section, the offloading outage performance for the paired users under ipCSI/pCSI conditions in the uplink NOMAMEC system is analyzed. Firstly, we derive the exact closedform expressions of the offloading outage probability and the asymptotic offloading outage probability in the high SNR region for the users. Then, so as to further study the outage performance in NOMAMEC, we obtain the diversity orders and evaluate the performance indicators of users such as system throughput and energy efficiency.
Outage probability
Considering that target rates for two users are determined by their QoS, the offloading outage probability becomes a prime indicator to evaluate the system performance. The offloading outage means that the user cannot complete offloading to the MEC server within the specified time. Hence, in uplink NOMAMEC scenario, the offloading outage performance for the users under ipCSI/pCSI conditions is analyzed in detail.
When the nth user completes N_{n}bits offloading tasks within T_{1}, the target transmission rate v_{n} of the nth user is denoted by \({v_{n}} = \frac {{{N_{n}}}}{{{T_{1}}}}\). Once the actual transmission rate R_{n} is less than v_{n}, the nth user has an outage behavior, and then, the offloading outage probability of the nth user under ipCSI is given by:
Theorem 1
The exact closedform expression for offloading outage probability of the nth user under ipCSI condition in NOMAMEC system is given by:
where \(\phantom {\dot {i}\!}\kappa = {2^{{v_{n}}}}  1, \varpi = 1\).
Proof
The SINR of the nth user Γ_{n} can be obtained by (3), and (4) is rewritten as:
Additionally, the offloading outage probability of the nth user is given by:
h_{m}^{2} and h_{n}^{2} are independent random variables that obey variances Ω_{m} and Ω_{n}, respectively, and with the aid of order statistics [31] and binomial theorem, the PDF of the nth user’s sorted channel gain h_{n}^{2} can be expressed as:
Substituting (8) into (7) and performing some simple operations, we can attain (5), which completes the proof. □
Corollary 1
Substituting ϖ=0 into (5), the exact closedform expression for offloading outage probability of the nth user under pCSI condition is given by:
The offloading outage event of the mth user can be expressed that the MEC server first decodes the task x_{m} by treating the task x_{n}. At this moment, an offloading outage event occurs when the actual transmission rate R_{m}= log(1+Γ_{m}) is lower than the transmission rate \({v_{m}} \left ({v_{m}} = \frac {{{N_{m}}}}{{{T_{1}}}}\right)\). Hence, the offloading outage probability of the mth user with ipCSI can be expressed as:
The offloading outage probability of the mth user in the NOMAMEC system will be given below.
Theorem 2
The exact closedform expression for offloading outage probability of the mth user under ipCSI condition in NOMAMEC system is given by:
where \(\phantom {\dot {i}\!}\chi {\mathrm { = }}{2^{{v_{m}}}}  1, \varpi = 1\).
Proof
See the Appendix. □
Corollary 2
By substituting ϖ=0 into (11), the exact closedform expression for offloading outage probability of the mth user under pCSI condition is given by:
Diversity order
In this subsection, we obtain the diversity orders of users under the different channel state conditions, which is defined as follows:
where P^{∞}(ρ) represents the offloading outage probability at high SNR of the users.
Corollary 3
When ρ→∞ is substituted into (5), with ρ→∞(x→0),1−e^{−x}∼x, and the nth user’s asymptotic offloading outage probability in the high SNR region under the ipCSI condition is given by:
Remark 1
Substituting (14) into (13), the diversity order for the nth user under ipCSI condition \({\mu _{\text {ipCSI}}^{n}}{\mathrm { = 0}}\) can be obtained.
Corollary 4
Substituting ρ→∞ into (9), the nth user’s asymptotic offloading outage probability in the high SNR region under the pCSI condition is given by:
Remark 2
Substituting (15) into (13), the diversity order for the nth user under pCSI condition \({\mu _{\text {pCSI}}^{n}} = n \) can be obtained.
Corollary 5
Substituting ρ→∞ into (11), the mth user’s asymptotic offloading outage probability in the high SNR region under the ipCSI condition is given by:
Proof
When ρ→∞(x→0), we have \({e^{ {\kern 1pt} \frac {{s\chi \left ({{\theta _{n}} + {\theta _{m}} + 1} \right)}}{{{a_{m}}\rho {\Omega _{m}}}}}} \sim {\mathrm {1}}  \frac {{s\chi \left ({{\theta _{n}} + {\theta _{m}} + 1} \right)}}{{{a_{m}}\rho {\Omega _{m}}}}\). By substituting it into (11), (16) can be determined. The proof is completed. □
Remark 3
Substituting (16) into (13), the diversity order for the mth user under ipCSI condition \({\mu _{\text {ipCSI}}^{m}}{\mathrm { = 0}}\) can be obtained.
Corollary 6
Substituting ρ→∞ into (12), the mth user’s asymptotic offloading outage probability in the high SNR region under the pCSI condition is given by:
Remark 4
Substituting (17) into (13), the diversity order for the mth user under pCSI condition \({\mu _{\text {pCSI}}^{m}}{\mathrm { = 0}}\) can be obtained.
Throughput analysis
In this subsection, the system throughput of NOMAMEC in the delaylimited transmission mode is discussed. The paired users offload tasks to the MEC server at constant rates of v_{m} and v_{n}, respectively.
Under the condition of channel estimation error, the throughput for the users in NOMAMEC system can be expressed as:
where \({\mathrm {P}_{\text {ipCSI}}^{n}}\) and \({\mathrm {P}_{\text {ipCSI}}^{m}}\) have been derived in (5) and (11), respectively.
In the absence of channel estimation error, the throughput for the users in NOMAMEC system can be expressed as:
where \({\mathrm {P}_{\text {pCSI}}^{n}}\) and \({\mathrm {P}_{\text {pCSI}}^{m}}\) have been derived in (9) and (12), respectively.
Energy efficiency
In this subsection, the energy efficiency in NOMAMEC system is analyzed based on the system throughput analysis above. Energy efficiency [32] is defined as:
In this system, the total data rate is expressed as the corresponding system throughput, and the total energy consumption can be expressed as the sum of two users’ transmitted power. According to the results derived above, the system energy efficiency under the ipCSI and pCSI conditions is expressed as follows:
and
respectively, where T represents the transmission time of the entire offloading process and η_{ipCSI} and η_{pCSI} are the energy efficiency of the system with or without channel estimation errors respectively in the delaylimited transmission mode.
Results and discussion
In this section, the numerical results are given to verify the above theoretical expressions derived. The performance under the ipCSI and pCSI conditions in NOMAMEC system is further evaluated. Assume that the distance from the MEC server to the nth user is d_{n}=0.3 m, while the distance from the mth user is d_{m}=0.7 m. The path loss exponent is set to α=2, and the power allocation factors are a_{n}=0.2 and a_{m}=0.8. We assume that the target transmission rates of this system are set to v_{n}=3 bit/s and v_{m}=0.1 bit/s, respectively. Compared with the performance of the traditional OMA, the entire communication process of TDMA is completed in two time slots. In other words, the mth and nth users occupy one time slot each in the system.
Figure 2 depicts the offloading outage probability for the two users versus the transmit SNR while the channel estimation errors are \({{\sigma }_{e_{n}}^{2}}{\mathrm { = }}10\)dB and \({{\sigma }_{e_{m}}^{2}}{\mathrm { = }} 0\) dB. The exact theoretical curves for the offloading outage probability of the two users under the ipCSI/pCSI conditions are plotted according to (5), (9) and (11), (12), respectively. It is clear that the exact curves clearly match the simulation curves. The offloading outage probability of the mth user is lower than the nth user’s probability at low SNR, and the opposite is true at the high SNR. Error floors exit with the users under the ipCSI condition because of the interference of channel estimation errors during transmission. Meanwhile, the offloading performance of the nth user is higher than that in TDMAMEC under the same conditions. Hence, the existence of channel estimation errors must be considered in the actual NOMAMEC scenarios.
As shown in Fig. 3, we present the system throughput versus the SNR under ipCSI/pCSI conditions in delaylimited transmission mode, and the channel estimation errors are \({{\sigma }_{e_{n}}^{2}}{\mathrm { = }} 0\) dB and \({{\sigma }_{e_{m}}^{2}}{\mathrm { = }}10\) dB. The solid curves are the throughput in the NOMAMEC system with or without channel estimation error, in which obtained according to (18) and (19). The dashed curve represents the throughput in the TDMAMEC system with or without channel estimation error. It is observed that with increasing the \({{\sigma }_{e_{i}}^{2}}\), the system throughput of TDMAMEC with ipCSI is becoming much smaller. This is due to the fact that the channel estimate error \({{\sigma }_{e_{i}}^{2}}\) leads to the worse offloading outage probability. Additionally, we can observe that channel estimation errors affect the performance index of this system, because the offloading outage probability for the users under pCSI is lower than that under ipCSI. The results show that with the \({{\sigma }_{e_{n}}^{2}}\) value increases, the offloading outage probability of the users increases, but the system throughput at the high SNR region decreases.
In Fig. 4, the offloading outage probability for the two users with channel estimation errors from \({{\sigma }_{e_{n}}^{2}}{\mathrm { = }}{{\sigma }_{e_{m}}^{2}}{\mathrm { = }}0\) dB to \({{\sigma }_{e_{n}}^{2}}{\mathrm { = }}{{\sigma }_{e_{m}}^{2}}{\mathrm { = }}  10\) dB is shown. We can observe that error floors exist under the ipCSI condition, which verify the conclusions in Remark 1 and Remark 3. The offloading outage probability gradually increases with the increase of the channel estimation error values. We can also see that the impact on the nth user is more obvious than the mth user because of the interference of the nth user and the channel estimation error. By contrast, the nth user is only interfered by the channel estimation error.
In Fig. 5, the system energy efficiency versus the SNR for the two users under ipCSI/pCSI conditions in delaylimited transmission mode is shown. The solid curves represent the energy efficiency for the NOMAMEC system which are obtained from (18), (21) and (19), (22) with the throughput. The energy efficiency for the NOMAMEC system is much higher than that of TDMAMEC. At high SNR, the energy efficiency of the NOMAMEC system with channel estimation error is higher than that of the TDMAMEC system without channel estimation error, because NOMAipCSI can achieve greater throughput than TDMApCSI in such transmission mode.
In Fig. 6, the offloading outage probability for the two users versus offloading times from 1 S to 2 S is shown. It is clear that when users are allowed less time to offload, the offloading outage probabilities will be increased. This is due to the smaller the offloading time is, the higher the target transmission rate of the users, and the greater the offloading outage probability is. Therefore, the offloading time must be considered in actual NOMAMEC systems.
In Fig. 7, we present the offloading outage probability for the two users versus various values of tasks. At N_{n}=4 bits, N_{m}=0.2 bits; N_{n}=3 bits, N_{m}=0.1 bits; and N_{n}=2 bits, N_{m}=0.05 bits, we can observe that with offloading tasks of both the nth and mth users increase simultaneously, the offloading outage probability also increases gradually. This is because that with the amount of tasks increases, the requirements for system performance are becoming higher. Hence, it is also necessary to consider the offloading tasks in NOMAMEC.
Figure 8 plots the offloading outage probabilities for the two users versus various values of the ith user. In Fig. 8a, m=2 and the values of n are 3, 4, and 5, while in Fig. 8b, n=4 and the values of m are 1, 2, and 3. We can observe that when the user is closer to the MEC server, the outage probability is becoming smaller. This is consistent with the fact that MEC is closer to the mobile devices.
Conclusions
We have investigated the offloading performance of uplink NOMAbased MEC with ipCSI/pCSI. The exact and asymptotic expressions of offloading outage probability for the paired users were derived in detail. The analytical results have shown that the offloading probability of NOMAMEC with pCSI is superior to TDMAMEC. As a result of channel estimation errors, the offloading behaviors of NOMAMEC with ipCSI are worse than that of pCSI. When the channel estimation errors increase, the offloading outage probability of NOMAMEC is becoming larger. Finally, the throughput and energy efficiency of NOMAMEC have been investigated with ipCSI/pCSI. In addition, the impact on the outage behaviors for users when the offloading time or tasks change has also been discussed.
Appendix: Proof of Theorem 2
By substituting (2) into (10), the offloading outage probability \({\mathrm {P}_{\text {ipCSI}}^{m}} \) can be given by:
Furthermore, the above equation can be calculated as:
With some arithmetic operations, the above expression can be given by:
h_{m}^{2} and h_{n}^{2} are independent random variables that obey variances Ω_{m} and Ω_{n}, respectively, and with the aid of order statistics and binomial theorem, the CDF of the mth user’s sorted channel gain h_{m}^{2} can be expressed as:
Substituting (26) into (25), the offloading outage probability of the mth user is given by:
The PDF of the nth user’s sorted channel gain h_{n}^{2} is known, and substituting it into the above expression can obtain the offloading outage probability as follows:
By sorting the above expression further, (11) can be attained easily. The proof is completed.
Notes
 1.
The superposed signals for multiple users can be mapped to single physical resource element or multiple elements. Based on these, NOMA can be divided into single carrier NOMA (SCNOMA) and multicarrier NOMA [2]. In this paper, we focus on single carrier NOMA and use NOMA to represent SCNOMA.
Abbreviations
 URLLC:

Ultrareliable and low latency communications
 OMA:

Orthogonal multiple access
 NOMA:

Nonorthogonal multiple access
 SIC:

Successive interference cancelation
 pCSI:

Channel state information
 QoS:

Quality of service
 ipCSI:

Imperfect channel state information
 MEC:

Mobile edge computing
 SNR:

Signaltonoise ratio
 AWGN:

Additive white Gaussian noise
 SINR:

Signaltointerferenceplusnoise ratio
 CPU:

Central processing unit
 TDMA:

Time division multiple address
References
 1
C. Y. She, R. Dong, Z. Y. Gu, Z. W. Hou, Y. H. Li, W. Hardjawana, C. Y. Yang, L. Y. Song, V. B, Deep learning for ultrareliable and lowlatency communications in 6G networks. IEEE, Networks,. https://arxiv.org/abs/2002.11045. Accessed 22 Feb 2020.
 2
X. W. Yue, Z. J. Qin, Y. W. Liu, S. L. Kang, Y. Chen, A unified framework for nonorthogonal multiple access. IEEE Trans. Commun.66(11), 5346–5359 (2018).
 3
Z. G. Ding, Y. W. Liu, J. Choi, Q. Sun, M. Elkashlan, I. ChinLin, H. V. Poor, Application of nonorthogonal multiple access in LTE and 5G networks. IEEE Commun. Mag.55(2), 185–191 (2017).
 4
Y. W. Liu, Z. J. Qin, M. Elkashlan, Z. G. Ding, A. Nallanathan, L. Hanzo, Nonorthogonal multiple access for 5G and beyond. arXiv preprint arXiv:1808.00277 (2018).
 5
Z. G. Ding, Z. Yang, P. Z. Fan, H. V. Poor, On the performance of nonorthogonal multiple access in 5G systems with randomly deployed users. IEEE Sig. Process Lett.21(12), 1501–1505 (2014).
 6
L. P. Zhu, J. Zhang, Z. Y. Xiao, X. B. Cao, D. O. Wu, Optimal user pairing for downlink nonorthogonal multiple access (NOMA). IEEE Wirel. Commun. Lett.8(2), 328–331 (2018).
 7
M. Amjad, L. Musavian, in IEEE Globecom Workshops (GC Wkshps). Performance analysis of NOMA for ultrareliable and lowlatency communications (IEEEAbu Dhabi, 2018), pp. 1–5.
 8
J. M. Kang, I. M. Kim, Optimal user grouping for downlink NOMA. IEEE Wirel. Commun. Lett.7(5), 724–727 (2018).
 9
N. B. Zhang, J. Wang, G. X. Kang, Y. Liu, Uplink nonorthogonal multiple access in 5G systems. IEEE Commun. Lett.20(3), 458–461 (2016).
 10
R. Nasfi, A. Chorti, in Eleventh International Conference on Ubiquitous and Future Networks (ICUFN). Performance analysis of the uplink of a two user NOMA network under QoS delay constraints (IEEEZagreb, 2019), pp. 526–528.
 11
X. W. Yue, Y. W. Liu, Y. Y. Yao, X. H. Li, R. Liu, A. Nallanathan, Secure communications in a unified nonorthogonal multiple access framework. IEEE Trans. Wirel. Commun.19(3), 2163–2178 (2020).
 12
Z. Yang, Z. G. Ding, P. Z. Fan, G. K. Karagiannidis, On the performance of nonorthogonal multiple access systems with partial channel information. IEEE Trans. Commun.64(2), 654–667 (2016).
 13
G. F. Pan, H. J. Lei, Y. S. Deng, L. S. Fan, J. Yang, Y. F. Chen, Z. G. Ding, On secrecy performance of MISO SWIPT systems with TAS and imperfect CSI. IEEE Trans. Commun.64(9), 3831–3843 (2016).
 14
C. Y. She, C. Y. Yang, T. Q. S. Quek, Crosslayer optimization for ultrareliable and lowlatency radio access networks. IEEE Trans. Wirel. Commun.17(1), 127–141 (2018).
 15
C. Y. She, C. Y. Yang, T. Q. S. Quek, Radio resource management for ultrareliable and lowlatency communications. IEEE Commun. Mag.55(6), 72–78 (2017).
 16
J. H. Liu, Q. Zhang, Offloading schemes in mobile edge computing for ultrareliable low latency communications. IEEE Access. 6:, 12825–12837 (2018).
 17
S. Wang, X. Zhang, Y. Zhang, L. Wang, J. W. Yang, W. B. Wang, A survey on mobile edge networks: convergence of computing, caching and communications. IEEE Access. 5:, 6757–6779 (2017).
 18
M. Chiang, T. Zhang, Fog and IoT: an overview of research opportunities. IEEE Internet Things J.3(6), 854–864 (2016).
 19
G. P. Fettweis, The tactile internet: applications and challenges. IEEE Veh. Technol. Mag.9(1), 64–70 (2014).
 20
K. Amemiya, Y. Akiyama, K. Kobayashi, Y. Inoue, S. Yamamoto, A. Nakao, in IEEE 7th International Conference on Cloud Networking (CloudNet). Onsite evaluation of a software cellular based MEC system with downlink slicing technology (IEEETokyo, 2018), pp. 1–7.
 21
H. Y. Yu, Q. Y. Wang, S. T. Guo, in IEEE International Conference on Networking, Architecture and Storage (NAS). Energyefficient task offloading and resource scheduling for mobile edge computing (IEEEChongqing, 2018), pp. 1–4.
 22
Z. G. Ding, P. Z. Fan, H. V. Poor, Impact of nonorthogonal multiple access on the offloading of mobile edge computing. IEEE Trans. Commun.67(1), 375–390 (2018).
 23
F. Wang, X. Zhang, in IEEE International Conference on Communications (ICC). Dynamic computation offloading and resource allocation over mobile edge computing networks with energy harvesting capability (IEEEKansas, 2018), pp. 1–6.
 24
Y. Wu, K. J. Ni, C. Zhang, L. P. Qian, D. H. K. Tsang, Nomaassisted multiaccess mobile edge computing: a joint optimization of computation offloading and time allocation. IEEE Trans. Veh. Technol.67(12), 12244–12258 (2018).
 25
A. Kiani, N. Ansari, Edge computing aware NOMA for 5G networks. IEEE Internet Things J.5(2), 1299–1306 (2018).
 26
Y. J. Pan, M. Chen, Z. H. Yang, N. Huang, M. ShikhBahaei, Energyefficient NOMAbased mobile edge computing offloading. IEEE Commun. Lett.23(2), 310–313 (2018).
 27
Z. G. Ding, D. W. K. Ng, R. Schober, H. V. Poor, Delay minimization for NOMAMEC offloading. IEEE Sig. Process. Lett.25(12), 1875–1879 (2018).
 28
Y. H. Ye, G. Y. Lu, R. Q. Hu, L. Q. Shi, in IEEE International Conference on Communications Workshops (ICC Workshops). On the performance and optimization for MEC networks using uplink NOMA (IEEEShanghai, 2019), pp. 1–6.
 29
P. T. Yang, L. X. Li, W. Liang, H. S. Zhang, Z. G. Ding, in 28th Wireless and Optical Communications Conference (WOCC). Latency optimization for multiuser NOMAMEC offloading using reinforcement learning (IEEEBeijing, 2019), pp. 1–5.
 30
X. B. Diao, J. C. Zheng, Y. Wu, Y. M. Cai, Joint computing resource, power, and channel allocations for D2Dassisted and NOMAbased mobile edge computing. IEEE Access. 7:, 9243–9257 (2019).
 31
H. A. David, H. N. Nagaraja, Order Statistics (John Wiley, New York, 2004).
 32
X. W. Yue, Y. W. Liu, S. L. Kang, A. Nallanathan, Z. G. Ding, Exploiting full/halfduplex user relaying in NOMA systems. IEEE Trans. Commun.66(2), 560–575 (2018).
Acknowledgements
The authors thank the anonymous reviewers for their constructive comments and suggestions. This work is supported in part by the Natural Science Foundation of Beijing Municipality under grants 4204099, 19L2022, L182032, L182039, and KZ201911232046; in part by the Science and Technology Project of Beijing Municipal Education Commission under grants KM202011232002 and KM202011232003; in part by the Key Research and Cultivation Project at Beijing Information Science and Technology University under grants 5211910924 and 5211910926; and in part by the Supplementary and Supportive Project for Teachers at Beijing Information Science and Technology University under grants 5111911147 and 5029011103.
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Jiang, H., Wang, Y., Yue, X. et al. Performance analysis of NOMAbased mobile edge computing with imperfect CSI. J Wireless Com Network 2020, 138 (2020). https://doi.org/10.1186/s13638020017500
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Keywords
 Mobile edge computing
 Nonorthogonal multiple access
 Imperfect channel state information
 Offloading outage probability