Power-Efficient Resource Allocation for MC-NOMA with Statistical Channel State Information

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1 Power-Efficient Resource Allocation for MC-NOMA with Statistical Channel State Inforation Zhiqiang Wei, Derrick Wing Kwan Ng, and Jinhong Yuan School of Electrical Engineering and Telecounications, The University of New South Wales, Australia arxiv:607.06v [cs.it] 5 Jul 06 Abstract In this paper, we study the power-efficient resource allocation for ulticarrier non-orthogonal ultiple access MC- NOMA systes. The resource allocation algorith design is forulated as a non-convex optiization proble which takes into account the statistical channel state inforation at transitter and quality of service QoS constraints. To strike a balance between syste perforance and coputational coplexity, we propose a suboptial power allocation and user scheduling with low coputational coplexity to iniize the total power consuption. The proposed design exploits the heterogeneity of QoS requireent to deterine the successive interference cancellation decoding order. Siulation results deonstrate that the proposed schee achieves a close-to-optial perforance and significantly outperfors a conventional orthogonal ultiple access OMA schee. I. INTRODUCTION Non-orthogonal ultiple access NOMA has been recognized as a proising ultiple access technique for the fifth-generation 5G wireless networks due to its high spectral efficiency and user fairness []. Copared to conventional orthogonal ultiple access OMA, NOMA transission allows ultiple users to share the sae frequency resource via exploiting the power doain ultiplexing and perforing successive interference cancellation SIC at the receiver side. It has been shown that NOMA offers considerable perforance gains over OMA in previous works [] [8]. In particular, resource allocation of NOMA has received significant attention since it is critical for the perforance of NOMA. In [6], [7], the authors evaluated the systelevel perforance of NOMA systes. The authors in [8] studied a iniu total transission power beaforing proble. In [9], the optial resource allocation for ultipleinput ultiple-output MIMO NOMA systes to axiize the instantaneous su-rate was proposed. However, existing works [6] [9] on resource allocation of NOMA have relied on the assuption of perfect channel state inforation at transitter CSIT which is difficult to obtain in practice. Recently, the notion of iperfect CSIT in NOMA systes for resource allocation algorith design has been pursued in [0] [4] under various syste perforance etrics. In [0], for a fixed power allocation, the outage probability and ergodic su-rate of NOMA under statistical CSIT were investigated in a cellular downlink scenario with randoly deployed users. In [], the authors analyzed the perforance degradation on these two syste perforance etrics due to partial CSIT. The authors in [] investigated the ipact of user pairing on This work was supported in part by the Australian Research Council ARC Linkage Project LP the su-rate of NOMA for a fixed power allocation schee. Power allocation was proposed for the axiization of the ergodic capacity and the iniization of the axiu outage probability in [3] and [4] under statistical CSIT, respectively. Apart fro those perforance etrics entioned above, power efficiency is also iportant due to the rising energy costs and green counication concerns. In [5], the authors solved the energy efficiency optiization proble for singlecarrier NOMA systes. Yet, if ulticarrier NOMA MC- NOMA systes are considered, the result fro [5] ay no longer be applicable. In [6] [8], various power allocation and user scheduling algoriths were proposed to axiize the su-rate of MC-NOMA systes. However, the results fro [6] [8] were based on perfect CSIT assuption which ay not available in practice, especially for MC-NOMA systes overloaded with exceedingly nuber of users. In addition, the aforeentioned works have not taken into account the heterogeneous quality of service QoS requireents, which play an iportant role in 5G networks, in particular for sall cells and assive access. In fact, power-efficient resource allocation based on statistical CSIT for MC-NOMA systes has not been reported in the literature so far. In this paper, we focus on the power-efficient resource allocation for MC-NOMA systes with QoS constraints under statistical CSIT. Due to the absence of perfect CSIT, a SIC policy taking consideration of QoS requireents is proposed, where the BS only allows one user to perfor SIC. Based on the adopted SIC policy, we forulate the resource allocation proble for MC-NOMA systes to iniize the total transit power. Since the optiization proble is a ixed cobinatorial non-convex proble, a suboptial solution is proposed to solve the power allocation and the user scheduling probles separately. For a given user scheduling policy, the ulticarrier power allocation proble is siplified to a persubcarrier basis power allocation proble which facilitates the optial power allocation design. Interestingly, based on the derived power allocation solution, an explicit etric for SIC decoding order associated with the level of QoS stringency is obtained, as an analogous to the channel gain based SIC decoding order for NOMA with perfect CSIT [6], [7]. In addition, we have quantified the perforance gain of NOMA over OMA in ters of power reduction and shown that the gain increases when the ultiplexed users have ore distinctive QoS stringency levels. For the user scheduling proble, a low coputational coplexity suboptial scheduling algorith based on aggloerative hierarchical clustering is proposed, which can achieve a close-to-optial perforance. Siulation results show that the proposed schee significantly increases

2 Base Station User Power... Frequency User... SICofUser's signal User 's signal decoding User 's signal decoding Fig.. A ulticarrier downlink NOMA syste where two users are ultiplexed on one subcarrier in NOMA with perfect CSIT [9]. User has a better channel quality who perfors SIC to decode and reove the signal of user before decoding its desired signal. The allocated power for user is higher than user. the power efficiency copared to a conventional OMA schee. The rest of the paper is organized as follows. Section II presents the syste odel and discusses the SIC policy with statistical CSIT. In Section III, we forulate the resource allocation as a non-convex optiization proble with QoS constraints. Section IV and Section V present the solution for power allocation and user scheduling, respectively. Siulation results are presented and analyzed in Section VI. Finally, Section VII concludes this paper. Notations used in this paper are as follows. Boldface lower case letters denote vectors. C denotes the set of coplex value; R M denotes the set of all M vectors with real entries; Z M denotes the set of all M vectors with integer entries; denotes the absolute value of a coplex scalar; Pr{ denotes the probability of a rando event. The circularly syetric coplex Gaussian distribution with ean µ and variance σ is denoted by CNµ,σ ; the unifor distribution in the interval [a,b] is denoted by U[a,b]; and stands for distributed as. II. SYSTEM MODEL In this section, we present the syste odel and the adopted assuptions for the considered MC-NOMA syste. A. Multicarrier NOMA Syste A ulticarrier downlink NOMA syste with one base station BS and K downlink users is considered, cf. Figure. All transceivers are equipped with a single-antenna. M subcarriers are provided to serve the K users. In this paper, to provide fairness in resource allocation, we assue that only L subcarriers are allocated to one user. In addition, we assue that each of the M orthogonal subcarriers is allocated to at ost two users to reduce the coputational coplexity and delay incurred at receiver side due to the SIC decoding, i.e., KL M. According to the NOMA protocol [7], on subcarrier {,...,M, the BS transits the essages of user i and j, i.e., s i and s j, with transit power p i and p j, i, j {,..., K, respectively. The corresponding transitted signal is represented by x = p i s i + p j s j. The received signal at user i {,...,K on subcarrier is given by y i = h i x +z i, where zi CN0,σ denotes the additive white Gaussian noise AWGN on subcarrier at user i. Variable h i C represents the channel coefficient including the joint effect of large scale fading and sall scale fading, i.e., h i = g i +d α i and gi CN0,, with d i denoting the distance between user i to the BS and α denoting the path loss exponent. We assue that the channel gain of sall scale fading is Rayleigh distributed and the path loss inforation is known at the BS due to long ter easureent. The cuulative distribution function CDF of channel gain of user i on subcarrier is given by F h i x = e +dα i x, x 0. 3 B. Successive Interference Cancellation Policy NOMA exploits the power doain to perfor ultiple access [3], [0], [0]. Based on the availability of CSIT, the BS perfors user scheduling and power allocation. Besides, SIC will be perfored at soe of the downlink users to itigate ulti-user interference, cf. Figure. In the literature [6], [8], [9], [9], with perfect CSIT and without QoS consideration, the user with better channel quality strong user decodes and reoves essage of user weak user before decoding its own, while the weak user directly decodes its own essage by treating the signal fro the strong user as noise. Furtherore, the BS will allocate ore power to the weak user to obtain fairness and facilitate SIC process. Unfortunately, without perfect CSIT, the BS cannot decide the SIC decoding order based on the ordered channel gain inforation. Siilar to the case of NOMA with perfect CSIT, distance ight be a criterion to define a strong or weak user. However, this criterion does not take consideration of QoS requireents, which also affect the SIC decoding order and hence change the behavior of power allocation. For exaple, if a user near the BS requires a lower outage probability, selecting this user to perfor SIC needs ore transit power than selecting the other user, which is in contrast to the case of conventional NOMA without considering the QoS requireents. On the other hand, it can be shown that for the case of NOMA with perfect CSIT and QoS requireents, both users perforing SIC will require ore transit power than selecting only the strong user to perfor SIC. Intuitively, the allocated power for both users will be increased to cope with the interference in decoding the other user s essage. Inspired by this fact, we assue that the BS only allows one user to perfor SIC on each subcarrier. Specifically, the BS will select user i to perfor SIC on subcarrier if the power consuption based on this selection is lower than that of selecting user j to perfor SIC. Latter in this paper, based on this assuption, an explicit SIC decoding order is derived with the level of QoS stringency. In addition, given the total required target rate for user j as R j, we can split it into L allocated subcarriers equally, since only statistical CSIT is available at the BS. Therefore, the target rate of user j on its allocated subcarrier is given by R j = R j 4 L and the corresponding target SINR is given by γ j = R j. 5

3 We assue that SIC at user i on subcarrier is successful when the achievable rate for decoding the essage of user j is not saller than the target rate of user j on subcarrier, i.e., R i j R j, 6 where Ri j denotes the achievable rate for user i to decode the essage of user j on subcarrier and it is given by Ri j = log + p j h i. 7 p i h i +σ III. PROBLEM FORMULATION In this section, we first define the QoS requireents and then forulate the power allocation and user scheduling proble for NOMA systes. A. Quality of Service QoS is usually defined by a target rate and a required outage probability. Given the target rate R i for each user on each allocated subcarrier, the QoS required by user i on subcarrier is given by the following outage probability constraint: { Pr Ri R i δi, i, 8 with { Ri R = i,i if Ri j R j, otherwise, R i,j where Ri and δi denote the achievable rate and the required outage probability of user i on subcarrier, respectively. Note that outage probability is defined on each subcarrier, which is coonly adopted in the literature for the siplification of resource allocation design [], []. Variables Ri,i and R i,j denote the achievable rates for user i on subcarrier with and without SIC, respectively, and they are given by Ri,i = log + p i h i σ and 0 Ri,j = log + p i h i, p j h i +σ respectively. B. Optiization Proble Forulation Now, the joint power allocation and user scheduling design for the MC-NOMA syste can be forulated as the following optiization proble: iniize p,c M { s.t. Pr Ri R i K K = i= j= p i 0, i,, K K c i,j,, d i= j= M K = j= c i,j c i,j c i,j p i +p j c i,j δ i, i,, b = L, i, e {0,, i,j,, f 9 a c where c i,j is the subcarrier allocation variable which is one if both user i and user j are ultiplexed on subcarrier, and will be zero otherwise. Vectors p R MK and c Z MK denote the collection of power allocation variables and user scheduling variables. Constraint b guarantees the QoS of all the users on their allocated subcarriers and it is inactive when user i is not allocated on subcarrier, i.e., c i,j = 0. Constraint c is non-negative constraint for power allocation variables. Constraints d and f are iposed to ensure that at ost two users are ultiplexed on one subcarrier and all the subcarriers are allocated to reduce the total power consuption. Constraint e is introduced for resource allocation fairness such that all the users have the sae aount of frequency resources. We note that, for the case of c i,j =, i = j, subcarrier is exclusively allocated to user i, and the user scheduling policy for subcarrier is degenerated to conventional orthogonal assignent. In other words, the proposed optiization fraework in generalizes the resource allocation for conventional OMA as a subcase. We note that the proble in is a ixed cobinatorial nonconvex proble, and there is no systeatic and coputational efficient approach to solve it optially. According to, the user scheduling is jointly affected by distance d i, target rate R i, and required outage probability δ i, while the counterpart of traditional NOMA with perfect CSIT depends only on channel gain order []. In addition, according to a and b, the power allocation and user scheduling variables are coupled. Therefore, in the following two sections, we propose a suboptial solution which intends to solve the power allocation and user scheduling separately. IV. SOLUTION FOR POWER ALLOCATION PROBLEM For a given user scheduling policy c that satisfies constraints d, e, and f, power allocation can be perfored independently on each subcarrier. Therefore, the original proble can be siplified to a per-subcarrier two-user power allocation proble. For notational siplicity, we drop the subcarrier index. The siplified optiization proble is given by iniize p i 3a p,p i= s.t. Pr {R i R i δ i, i {,, 3b p i 0, i {,, 3c where R i is given by 9. In the following, we first solve the proble in 3 by assuing only one user to perfor SIC, then derive the SIC decoding order based on power allocation solution, and copare its perforance with OMA. A. Power Allocation Solution The optial power allocation solution for the proble in 3 can be obtained via the following two cases. For the first case, we only allow user to perfor SIC and obtain the corresponding power allocation solution. The power allocation solution for the second case, which only allows user to perfor SIC, is also obtained. Then, the optial solution for the proble in 3 is given by the solutions for both cases with the lower power consuption.

4 According to 6, if we allow user to perfor SIC and prevent user to do that, the following prerequisites should be satisfied: p p γ > 0 and 4 p p γ 0. 5 We note that, due to the channel uncertainty, the prerequisite in 4 cannot guarantee the success of SIC and the success of SIC also cannot guarantee outage free transission. This akes the resource allocation for MC-NOMA in this paper fundaentally different fro the case of perfect CSIT. Under these two prerequisites, 4 and 5, the outage probability for both users are given by = Pr = Pr {R R,R, < R +Pr {R < R,R, < R, 6 {R, < R, 7 where and denote the outage probability of user and user, respectively. Equation 3b requires that i δ i. Note that consists of two ters which denote the outage probability with a successful SIC and an unsuccessful SIC at user, respectively. Substituting 7, 0, and into 6 and 7 yields { γ = Pr h σ γ σ < ax, and 8 p p p γ = Pr { h < γ σ, 9 p p γ respectively. Exploiting the CDF of channel gain 3 in 8 and 9, and substituting the into 3b, we obtain the solution of 3 with the iniized total transit power as: p = γ p = ax and 0 β γ γ + γ, γ γ + γ,, β β β β where β i = ln δi σ +d α i, p i, i {,, is the allocated power for user i for the first case, and the superscript denotes allowing user to perfor SIC. Note that β i can be interpreted as the level of QoS stringency for user i, where a large β i eans user i is far away fro the BS or has a sall required outage probability, such that a higher transit power is necessary to satisfy its stringent QoS requireent. Siilar to the case of NOMA with perfect CSIT, we can define a user with larger β i as a QoS non-deanding user and define the other user as a QoS deanding user. For the second case which allows user to perfor SIC and prevents user to do that, the prerequisites are given by p p γ > 0 and p p γ 0. Siilarly, the power allocation solution for 3 can be derived and given as γ γ p = ax + γ, γ γ + γ, and 3 β β β β β p = γ β, 4 β where the superscript denotes allowing user to perfor SIC. In suary, the optial solution for the proble in 3 can be selected by p,p = p,p p,p if p +p p +p, otherwise, 5 and the BS will infor user i to perfor SIC and forbid the other user to do that if is selected. p i,pi B. A Siple SIC Decoding Order The selection of optial power allocation in 5 incorporates the SIC decoding policy iplicitly to achieve iniu power consuption. However, we can obtain an explicit rule to deterine the SIC decoding order for a general condition of γ and γ, which eans that both users target rates are not saller than bit/s/hz. In such a condition, β and β will never be chosen in and 3, respectively. Thus, we have a siple solution for the joint optial SIC decoding order and power allocation: p p,p =,p if β β, p 6,p otherwise, which indicates that the QoS non-deanding user is always selected to perfor SIC to iniize the power consuption. Therefore, for a general condition of γ and γ, β i defines the optial SIC decoding policy in ters of power efficiency, where we only allow the QoS non-deanding user to perfor SIC to reduce the total power consuption. Note that for γ i <, we have to evaluate both solutions and copare the in 5 to find the SIC decoding order. C. Coparison between NOMA and OMA For the case of NOMA with perfect CSIT, it is well known that the perforance gain of NOMA over OMA increases when the differences in channel gains between the ultiplexed users becoe larger [6], [], [9]. In this paper, we can obtain a siilar conclusion with our schee in ters of power reduction for the case of iperfect CSIT. For a fair coparison, we ipose the sae spectral efficiency for NOMA and OMA, where a single subcarrier is further split into two subcarriers with equal bandwidth for the OMA case. Therefore, the power allocation for two OMA users with statistical CSIT on one subcarrier is given by p OMA,p OMA R = β, R β, 7 where the superscript OMA denotes the case of OMA. Now, we provide a sufficient condition that the power consuption of NOMA is no larger than that of OMA. Suppose R bit/s/hz and R bit/s/hz, we can obtain the perforance gain of NOMA over OMA in ters of power reduction as follows: p OMA total p NOMA total = γ β γ β β γ β γ β β + γ β γ β 0 if β β, + γ β γ β > 0 otherwise, 8

5 where p OMA total and p NOMA total denote the total power consuption of OMA and NOMA on a single subcarrier, respectively. It can be observed that under the sufficient condition, the power reduction of NOMA over OMA is non-negative. More iportantly, with R bit/s/hz and R bit/s/hz, the perforance gain of NOMA over OMA also increases when the difference in the level of QoS stringency or the target rate between the QoS deanding user and QoS nondeanding user becoe larger, e.g. β β or γ γ. Note that the total power consuption difference between NOMA and OMA is zero for the case of statistical CSIT when the ultiplexed users have identical distances and QoS requireents, i.e., β = β and γ = γ. In suary, fro 6 and 8, we conclude that the level of QoS stringency β i plays a significant role in power allocation and SIC decoding order design. V. USER SCHEDULING ALGORITHM According to, the K users can be treated as KL independent virtual users since their QoS constraints b are iposed on each subcarrier independently. In addition, NOMA provides significant syste perforance gain in high syste load scenario. Thus we focus on a practical overload scenario, i.e., KL > M. Now, to serve K users via M subcarriers, we intend to generate a user cobination consisting of KL M users pairs and M KL single users, which correspond to NOMA and OMA, respectively. In all candidate user cobinations, user scheduling needs to select one cobination which consues the inial power. Without loss of generality, we assue L = in this section. For L >, we siply eliinate the cobinations where one user is paired with itself to satisfy constraint e. As we entioned before, the power consuption of each subcarrier is only affected by the two ultiplexed users on it. To schedule K K user over M subcarriers, there are possible candidate pairs of users, and we can get the power consuption for all the pairs fro 5, i.e., p ij, i,j {,...,K and i j. In addition, for orthogonal subcarrier assignent, the power consuption for user i is given by p ii = γi β i. The nuber of all candidate cobinations is given by K M K N =. 9 M K = To obtain the optial user scheduling policy, we need to verify and copare all these N candidate cobinations, where N is prohibitively large even for oderate K and M. Thus, we attept to propose a heuristic user scheduling algorith based on the following geoetric illustration. Figure illustrates a user scheduling case with 4 users, where every point denotes a user, every line l ij denotes pairing user i and user j. The length of line l ij is given by p ij, which denotes the power consuption for pairing user i and user j. Note that it is an undirected graph, i.e., p ij = p ji since both p ij and p ji denote the power consuption for pairing user i and user j. Fro a iniu power consuption perspective, user i and user j are ore likely to be paired with each other if point i and point j are close and they are far away fro other points, such as point and point 3 in Figure. Based on this siple idea, the user scheduling proble becoes a Fig.. Distance l l 3 l 3 l 4 3 l 4 Geoetric illustration for the proposed user scheduling with 4 users l Point Fig. 3. Dendrogra for the case in Figure. clustering proble aong all the points on a two-diensional plane. Now, we apply aggloerative hierarchical clustering to build the hierarchy fro the individual points by progressively erging clusters [3]. Based on the length of all the lines l ij, we can obtain the dendrogra structure of all the points, which illustrates the arrangeent of clusters, cf. Figure 3. In the dendrogra, the vertical axis of a point denotes the average distance between this point with all the clusters below it, and the horizon axis presents the ordered points set in ters of distance to the clusters on the left of it. For exaple, Figure 3 illustrates a dendrogra for the case in Figure, where point3 is the nearest point to point, and point 4 is the farthest point to the cluster consists of points, 3, and. In other words, the horizon axis illustrates the ordered users set in ters of average power consuption for pairing with each user on its left. Note that the generated order in dendrogra is based on the joint effect of β i and γ i, which provides a rule of thub for user scheduling. According to 0,, 3, and 4, the power consuption of NOMA increases with the target SINR of both ultiplexed users. Thus we expect that the right M K users in the horizontal axis of the dendrogra are assigned on M K subcarriers exclusively to reduce the total syste power consuption since these users are usually QoS deanding. For the reaining left K M users, we need to generate K M pairs of users. Since the perforance gain over OMA increases with the difference of βi as well as γi βi between paired users, referring to 8, we intend to partition the reaining left K M users into two groups and pair the in successive order. For exaple, if we only have two subcarriers for the case of 4 users in Figure 3, we partition the into two groups, {,3 and {,4. Then we pair user with user and pair user 3 with user 4. The user scheduling 4

6 Algorith User Scheduling Algorith : Copute p ij, i j, i,j {,...,K, through 5. : Generate the dendrogra based on p ij via aggloerative hierarchical clustering [3]. 3: Allocate the right M K users on M K subcarriers exclusively. 4: Partition the left K M users into two groups and pair the in successive order on K M subcarriers. algorith is suarized in Algorith. Note that for the case of L >, each point in Figure will be replaced by L points which have the sae distance to all the other points due to our equally target rate assignent 4. Therefore, the dendrogra in Figure 3 will be extended by replacing each user with a cluster of L users of equal altitude. Therefore, our scheduling will avoid the pair of users where one user is paired with itself unless KL M =. For the case of KL M =, we will select the first point of the right M K users to pair to satisfy constraint e. We note that although the proposed user scheduling algorith is suboptial, it is ore coputational efficient copared to optial exhaustive search. In particular, the coplexity of aggloerative clustering algorith is only O K 3 in general case. Besides, the suboptiality of the proposed user scheduling algorith will be verified in the siulation section. VI. RESULTS In this section, the perforance of our proposed schee is verified with siulations. In a single-cell with BS located at the center with cell size D, there are K users randoly and uniforly distributed between 30 and D, i.e., d i U[30, D]. Siilarly, the target rates of all the users are generated by R i U[0., 0] bit/s/hz. In the following siulations, two kinds of outage probability are evaluated to copare the perforance gain by introducing the QoS constraints: Case I with equal outage probability δ i = 0 and Case II with rando outage probability δ i U[0 5, 0.]. The user noise power on each subcarrier is σ = 8 db. The 3GPP path loss odel with path loss exponent α = 3.6 is adopted in our siulations [4]. The siulation results shown in the sequel are averaged over 000 realizations of different user distances, target rates, ultipath fading coefficients, and outage probability requireents. A. Power Consuption versus Cell Size In Figure 4, we investigate the power consuption versus cell size D for the considered MC-NOMA syste with M = 5, K = 4, and L =. For coparison, we also show the perforance of OMA, rando scheduling and, full search scheduling. Note that power consuption for OMA is given with 7 by replacing R i with K/M R i since the available frequency bandwidth is split equally for K users. In addition, we note that the rando scheduling and the full search scheduling are perfored together with the proposed power allocation solution 5. It can be seen that Since the coputational coplexity of full search is extreely large, we adopt sall values for M, K, and L to copare our proposed schee with the full search scheduling. We note that our proposed schee is very coputational efficient copared to exhaustive search, which can apply to a scenario with ore users and subcarriers. Total power consuption db OMA Rando scheduling Proposed schee Full search scheduling Case I Case II Cell Size Fig. 4. Power consuption versus cell size. The results for Case I and Case II are illustrated with black color and blue color, respectively. The double-sided arrows illustrate the perforance gain of our proposed schee over OMA in Case I and Case II, respectively. Total power consuption db Case I OMA Rando scheduling Proposed schee Full search scheduling Case II Nuber of users Fig. 5. Total power consuption versus the nuber of users. The results for Case I and Case II are illustrated with black color and blue color, respectively. The double-sided arrows illustrate the perforance gain of our proposed schee over OMA in Case I and Case II, respectively. our proposed user scheduling ethod provides a significant power saving copared to the rando scheduling, and achieves a perforance close to the full search scheduling in both cases. The reason for this iproveent is that our proposed user scheduling ethod takes into account the joint effect of β i and γ i, and exploits the heterogeneity of QoS requireents, which achieves a better utilization of power doain. More iportantly, the perforance gain of our proposed schee over OMA in Case II is larger than Case I. This result deonstrates the effectiveness of our proposed schee in exploiting the QoS heterogeneity to reduce power consuption. B. Total Power Consuption versus Nuber of Users In Figure 5, we investigate the perforance of our proposed schee versus the nuber of users. A MC-NOMA syste with M = 5 subcarriers and cell size D = 00 is

7 considered. We assue L = in this case, and the nuber of users K varies fro 6 to 0. It can be observed that our proposed resource allocation schee reduces the power consuption substantially copared to the rando scheduling, and also perfors closely to the full search scheduling in both cases. Besides, it can be observed that the perforance gain of our proposed schee over OMA in Case II is also larger than that in Case I owing to a better resource utilization via taking into account the diversification of QoS requireents. More iportantly, it can be seen that the perforance gain over OMA increases with nuber of users in both cases, which is consistent with the case of NOMA with perfect CSIT. In fact, the QoS requireents and average user channel gain becoe ore heterogeneous for an increasing nuber of users. Thus the conventional OMA schee fails to accoodate the diverse needs, and our proposed schee will obtain ore perforance gain. We note that the power consuption of OMA is lower than that of rando scheduling for K = 6 and K = 7 but still higher than our proposed schee. Although NOMA significantly outperfors OMA in single subcarrier 8, MC- NOMA with rando scheduling ay consue ore power than OMA in such low overload ratio, e.g. K M. In fact, with low overload ratio, due to the user scheduling constraint e for fairness consideration, there are only few pairs of users in the user cobination, and thus MC-NOMA with rando scheduling cannot fully exploit the power doain. In addition, we note that the perforance gap between our proposed suboptial schee with the full search scheduling increases slightly with the nuber of users. However, the coputational coplexity of our proposed schee is significantly lower than that of the full search scheduling. VII. CONCLUSION In this paper, we studied the power-efficient resource allocation for MC-NOMA systes with statistical CSIT by taking into account the heterogeneity of QoS requireents. The resource allocation was forulated as a non-convex optiization proble to iniize the total power consuption. A low coputational coplexity suboptial solution was proposed to solve power allocation and user scheduling probles separately. We derived the power allocation solution and characterized an explicit etric to decide the SIC decoding order associated with the level of QoS stringency. Besides, under a sufficient condition, we showed that the perforance gain of NOMA over OMA in ters of power reduction increases with the difference in the level of QoS stringency between the ultiplexed users. For the user scheduling, a coputational efficient scheduling algorith based on aggloerative hierarchical clustering was proposed. 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