NOMA Aided Narrowband IoT for Machine Type Communications with User Clustering
NNOMA A
IDED N ARROWBAND I O T FOR M ACHINE T YPE C OMMUNICATIONS WITH U SER C LUSTERING A LI S HAHINI N IRWAN A NSARI
TR-ANL-2018-002 th December, 2018 A DVANCED N ETWORKING L ABORATORY D EPARTMENT OF E LECTRICAL AND C OMPUTER E NGINEERING N EW J ERSEY I NSTITUTE OF T ECHNOLOGY a r X i v : . [ c s . N I] D ec Abstract
To support Machine Type Communications (MTC) in next generation mobile networks, NarrowBand-IoT (NB-IoT) has beenreleased by the Third Generation Partnership Project (3GPP) as a promising solution to provide extended coverage and low energyconsumption for low cost MTC devices. However, the existing Orthogonal Multiple Access (OMA) scheme in NB-IoT cannotprovide connectivity for a massive number of MTC devices. In parallel with the development of NB-IoT, Non-Orthogonal MultipleAccess (NOMA), introduced for the fifth generation wireless networks, is deemed to significantly improve the network capacity byproviding massive connectivity through sharing the same spectral resources. To leverage NOMA in the context of NB-IoT, wepropose a power domain NOMA scheme with user clustering for an NB-IoT system. In particular, the MTC devices are assignedto different ranks within the NOMA clusters where they transmit over the same frequency resources. Then, we formulate anoptimization problem to maximize the total throughput of the network by optimizing the resource allocation of MTC devices andNOMA clustering while satisfying the transmission power and quality of service requirements. We prove the NP-hardness of theproposed optimization problem. We further design an efficient heuristic algorithm to solve the proposed optimization problem byjointly optimizing NOMA clustering and resource allocation of MTC devices. Furthermore, we prove that the reduced optimizationproblem of power control is a convex optimization task. Simulation results are presented to demonstrate the efficiency of theproposed scheme.
Index Terms
NOMA, Narrowband-IoT, Resource Allocation.
I. I
NTRODUCTION I NTERNET of Things (IoT) is a world wide network of interconnected entities and is anticipated to grow in coming yearswith the projection of connecting as many as billions of devices with an average of 6-7 devices per person by 2020 [1], [2].There are three typical usage scenarios for fifth generation (5G) mobile network services, including enhanced mobile broadband(eMBB), massive machine type communications (mMTC) and ultra-reliable and low-latency communications (URLLC) [3].Different from eMBB, mMTC and URLLC mainly target services of IoT and are considered as two types of Machine TypeCommunications (MTC) characterized by the International Telecommunications Union (ITU). mMTC and URLLC devicesas two important enablers of IoT have different characteristics. mMTC requires connectivity of a massive number of activelow-power devices in co-existence in one cell, and these devices transmit small packets with relaxed latency requirements inthe order of seconds or hours [4]. Unlike mMTC, ultra reliable data transmissions is essential for URLLC devices along withlow latency requirements as they are used for critical applications [3].To support MTC for next generation mobile networks, a new technology called Narrow-band Internet of Things (NB-IoT)has recently been standardized by the Third Generation Partnership Project (3GPP) in its Release 13 [5]. In particular, NB-IoTprovides energy efficient communications for low power MTC devices on a narrow bandwidth of 180 kHz for both downlinkand uplink [6]. In order to provide better granularity and higher utilization, the unit of resource scheduling in the NB-IoTuplink is sub-carrier instead of Physical Resource Block (PRB). In fact, the NB-IoT uplink has sub-carrier spacing of 3.75 kHz,
The authors are with Advanced Networking Laboratory, the Helen and John C. Hartmann Department of Electrical and Computer Engineering, New JerseyInstitute of Technology, Newark, NJ 07102. E-mail: ali.shahini, [email protected]. This work is currently under review in IEEE Internet of Things Journal. i.e., the minimum transmission bandwidth for a device, whereas the downlink retains the Long Term Evolution (LTE) downlinktransmission structure with 15 kHz sub-carrier spacing [7]. NB-IoT can provide data rates of nearly 250 kbps in downlink and20 kbps in uplink transmissions with the possibility to aggregate multiple sub-carriers to reach the downlink speed [8], [9]. Thetarget of NB-IoT is to prolong the battery lifetime to reach 10 years and provide massive connectivity of devices [6]. However,the main challenge of providing connectivity to a massive number of MTC devices in 5G networks cannot be addressed byexisting NB-IoT technologies.Currently, NB-IoT exploits an orthogonal multiple access (OMA) scheme over a bandwidth of 180 kHz where each sub-carriercannot be occupied by more than one user. Thus, the OMA scheme in NB-IoT fails to cope with the massive increase in thenumber of connected MTC devices. Hence, to support connectivity to a massive number of MTC devices with the limitednumber of sub-carriers in one PRB, a promising solution is to adopt power-domain Non-Orthogonal Multiple Access (NOMA)scheme [10], [11]. In contrast with OMA methods, NOMA supports massive connectivity by allocating multiple MTC devicesto share each sub-carrier. In other words, multiple MTC devices can transmit over the same frequency resources, thus resultingin a significant increase in the network connectivity. In the power domain NOMA scenario, different power level strategy isconsidered to decode the differentiated messages sequentially at the receiver side [12]. In fact, the Successive InterferenceCancellation (SIC) [13] scheme is exploited at the receiver side to extract the transmitted messages. Thus, NOMA can helpNB-IoT systems to meet their demands of massive connectivities, and high spectral-energy efficiency.
A. Contributions
While there are several research activities that investigate NOMA techniques for 5G networks, none, to our best knowledge,has leveraged the advantages of NOMA in the context of NB-IoT with user clustering of different users with various quality ofservice (QoS) requirements. To this end, we aim to address the aforementioned issue by proposing a general system modelfocusing on two emerging technologies of NOMA and NB-IoT. In fact, we propose a novel NOMA based NB-IoT modelto maximize the total throughput of an NB-IoT network by increasing the number of connected devices through optimalclustering of MTC devices and optimizing the resource allocation. In particular, MTC devices are grouped into differentNOMA clusters and share the same frequency resources among the cluster members. Considering the intra-cell interferences,transmission power and QoS requirements, the MTC devices are ranked in each NOMA cluster. The goal is to maximize thetotal uplink transmission rate of MTC devices by optimizing NOMA clustering and resource allocation of MTC devices. Themain contributions of the paper include: • We propose a NOMA clustering method for MTC devices in an NB-IoT system. In particular, MTC devices are classifiedinto different NOMA clusters and the same frequency resources are shared among the cluster members. Considering theintra-cell interferences, transmission power and QoS requirements, the MTC devices are ranked in each NOMA cluster.Therefore, spectral resources are allocated to the NOMA clusters based on the requirements of NOMA cluster members. • We formulate a NOMA based optimization problem to maximize the total sum rate of uplink transmission in an NB-IoTsystem by optimizing the resource allocation of MTC devices and NOMA clustering while satisfying the transmissionpower and quality of service requirements. We further prove the NP-hardness of the proposed optimization problem. • We propose an efficient heuristic algorithm to solve the optimization problem by jointly optimizing NOMA clustering andresource allocation of MTC devices. Furthermore, we prove that the reduced optimization problem of power control is aconvex optimization task by introducing variable transformations. • We evaluate the performance of our proposal and the heuristic algorithm via simulations to demonstrate the benefits ofNOMA in increasing the total throughput of MTC devices in an NB-IoT system.
B. Related Works
In this section, related works including NB-IoT, NOMA, and resource allocation are discussed. In the past few years, severalworks investigated the major challenges of NB-IoT and researchers came up with different algorithms and models. Recently,Yang et al. [14] investigated the small-cell assisted traffic offloading for NB-IoT systems and formulated a joint traffic schedulingand power allocation problem to minimize the total power consumption. Oh and Shin [15] proposed an efficient small datatransmission scheme for NB-IoT in which devices that are in an idle state can transmit a small data packet without the radioresource control connection. Malik et al. [16] investigated radio resource management in NB-IoT systems by proposing aninterference aware resource allocation for the rate maximization problem.Al-Imari et al. [17] proposed a NOMA scheme for uplink data transmission that allows multiple users to share the samesub-carrier without any coding/spreading redundancy. Mostafa et al. [18] studied the connectivity maximization for the applicationof NOMA in NB-IoT, where only two users can share the same sub-carrier. Kiani and Ansari [19] proposed an edge computingaware NOMA technique in which MEC users’ uplink energy consumption is minimized via an optimization framework. Wu et al. [20] investigated the spectral efficiency maximization problem for wireless powered NOMA IoT networks. Shahini etal. [21] proposed the energy efficiency maximization problem for cognitive radio (CR) based IoT networks by taking intoconsideration of user buffer occupancy and data rate fairness. Qian et al. [22] proposed an optimal SIC ordering to minimizethe maximum task execution latency across devices for MEC-aware NOMA NB-IoT network. Zhai et al. [23] proposed a jointuser scheduling and power allocation for NOMA based wireless networks with massive IoT devices. Xu and Darwazeh [24]proposed a compressed signal waveform solution, termed fast-orthogonal frequency division multiplexing (Fast-OFDM), topotentially double the number of connected devices.Several works have investigated NOMA for 5G networks, but none has looked into employing NOMA clustering for NB-IoTusers with various QoS requirements. Therefore, we propose a novel NOMA based NB-IoT model to maximize the totalthroughput of the network by optimizing both NOMA clustering and the resource allocation of MTC devices in an NB-IoTsystem.The remainder of this paper is organized as follows. In Section II, we describe the system model including NOMA clusteringand QoS constraints. In Section III, we formulate the framework of the throughput maximization problem. In Section IV, wedetail the proposed algorithm. In Section V, numerical results and simulations are presented. Finally, we conclude the paper inSection VI.
Fig. 1. The NOMA clusters include mMTC and URLLC devices, where the allocated sub-channels to each NOMA cluster are shared by the MTC devices.
II. S
YSTEM M ODEL
We consider a single-cell scenario with one eNB, which supports MTC based on NB-IoT standard [5]. We assume there isno inter-cell interference from other neighboring cells. Denote U = { , ..., U } and M = { , ..., M } as the sets of mMTC andURLLC devices, respectively. Active URLLC and mMTC devices share one physical resource block (PRB) for uplink datatransmission in one transmission time interval (TTI). The available bandwidth of one PRB is assumed to be divided into a setof sub-channel frequencies S = { , ..., S } and the bandwidth of each sub-channel is W . In fact, the system bandwidth can beequally divided into either 48 or 12 sub-carriers in NB-IoT systems. In particular, the sub-carrier spacing of 3.75 kHz can onlybe supported for uplink transmissions [9]. Therefore, we consider one PRB with 48 sub-carriers of 3.75 kHz for the uplink datatransmissions.We propose a power-domain NOMA scheme by clustering mMTC and URLLC devices in an NB-IoT network as shown inFig. 1. According to the NOMA scheme, the mMTC and URLLC devices share each sub-carrier (sub-channel), and transmit datain a non-orthogonal manner, i.e., more than one user can share the same sub-channel. Therefore, the devices are divided intodifferent groups, called the NOMA clusters. Denote C = { , ..., C } as the set of NOMA clusters, and γ s,c as the binary variableto assign sub-channel s ∈ S to NOMA cluster c ∈ C . Hence, γ s,c = 1 if sub-channel s is allocated to the c th NOMA cluster,and γ s,c = 0 otherwise. The URLLC and mMTC devices transmit their messages on the same sub-channel with transmissionpowers of p u and p m , respectively. Thus, a combined message from URLLC and mMTC devices with additive noise N isreceived at the eNB. In order to successfully decode messages from the combined received message, the eNB employs the SICscheme. Thus, the users need to be ordered in each cluster according to the SIC method.Define the set of the order (ranks) in each cluster as K = { , ..., k max } , where k max specifies the maximum number ofusers that are allowed to be in one cluster and consequently share the allocated sub-channels. Note that we assume C × k max should be greater than the total number of the devices. According to the principles of SIC [13], the k th user’s message in eachcluster is decoded before the other users with higher orders. Therefore, the users with higher ranks ( { k + 1 , k + 2 , ... } ) in eachcluster introduce interference to the k th user. In other words, the user with the highest rank in each cluster does not experience TABLE IL
IST OF S YMBOL N OTATIONS AND D ESCRIPTION
Symbols Descriptions U ( M ) The set of URLLC users (the set of mMTC users) S The set of sub-channels in an NB-IoT system C ( K ) The set of NOMA clusters (the set of orders in each NOMA cluster) k max The maximum number of users in one NOMA cluster γ s,c The binary indicator whether to allocate the s th sub-channel to the c th cluster p su The transmission power of the u th URLLC device over the s th channel p sm The transmission power of the m th mMTC device over the s th channel N The Additive White Gaussian Noise α c,km The binary indicator whether to assign the m th mMTC to the k th order of cluster cβ c,ku The binary indicator whether to assign the u th URLLC to the k th order of cluster cR m The total transmission rate of the m th mMTC device R u The total transmission rate of the u th URLLC device W RB The total bandwidth of one resource block in the NB-IoT W The bandwidth of one tone in one RB h sm The channel gain of the m th mMTC device over the s th sub-channel h su The channel gain of the u th URLLC device over the s th sub-channel R thm The minimum transmission rate of the m th mMTC device R thu The minimum transmission rate of the u th URLLC device P maxm The maximum power budget of the m th mMTC device P maxu The maximum power budget of the u th URLLC deviceinterference from other users and the first user receives interference from other users with higher ranks ( k = 2 , ..., k max ). Notethat URLLC devices have higher data rate requirements as compared to mMTC devices. Thus, the transmission power ofURLLC devices are higher than that of mMTCs. Therefore, in each cluster, the URLLC devices are required to have lowerranks as compared to mMTC devices. In fact, the SIC decoder at the eNB starts decoding with URLLCs, and consequently themMTC devices are not affected by high interference from URLLCs. For the ease of reading, frequently used notations andterminologies are summarized in Table II-A. A. Quality of Service Constraints
Denote p sm as the transmission power of the m th mMTC over the s th sub-channel and α c,km as the binary variable to allocateof the m th mMTC to the k th order of cluster c . In fact, α c,km = 1 if there is an allocation, and α c,km = 0 otherwise. Thus,the achievable data rate of the m th mMTC device, R m , in terms of the aggregate rate over the allocated sub-carriers can beexpressed as R m = (cid:88) c ∈C (cid:88) k ∈K α c,km (cid:88) s ∈S γ s,c W log | h sm | p sm N W + (cid:80) d ∈M\ m k max (cid:80) h = k +1 α c,hd | h sd | p sd , (1)where N is the noise power spectral density and h sm denotes the channel gain between the m th mMTC device and the eNB onsub-channel s . Since the NOMA clustering procedure requires mMTC devices to have higher ranks as compared to URLLCs, the URLLC devices do not interfere mMTCs. Thus, the m th mMTC only experiences interference from the other mMTCs ofthe same cluster with higher ranks.Note that each mMTC device requires a threshold for its data rate to be greater than the minimal data rate of R thm , i.e., R m (cid:62) R thm , ∀ m ∈ M . (2)The total transmission power of the m th mMTC device is limited to its maximum power budget P maxm , i.e., (cid:88) s ∈S p sm (cid:54) P max m , ∀ m ∈ M . (3)Similarly, the achievable data rate of the u th URLLC device can be determined by the Shannon-Hartley theorem. Note that theranks of URLLCs are always greater than those of mMTCs in each NOMA cluster. Thus, they receive interference from all themMTC cluster members as well as those URLLC cluster members with higher ranks. Denote β c,ku as the binary variable toassign the u th URLLC to the k th order of cluster c . In other words, β c,ku = 1 if there is an allocation, and β c,ku = 0 otherwise.Therefore, the achievable data rate of the u th URLLC device over the allocated sub-carriers is shown in Eq. (4), where h su isthe channel gain between the u th URLLC device and the eNB on sub-channel s , and p su represents the transmission power ofthe u th URLLC over the s th sub-channel. Owing to performing critical tasks by URLLC devices, their power consumption isnot of significant importance. Thus, the transmission powers of URLLC devices are set to their maximum limit, i.e., R u = (cid:88) c ∈C (cid:88) k ∈K β c,ku (cid:88) s ∈S γ s,c W log | h su | p su N W + (cid:80) d ∈U\ u k max (cid:80) h = k +1 β c,hd | h sd | p sd + (cid:80) m ∈M k max (cid:80) h = k +1 α c,hm | h sm | p sm , (4) (cid:88) s ∈S p su = P max u , ∀ u ∈ U . (5)Meanwhile, the data rate of the u th URLLC device should be greater than a given minimal rate R thu , R u (cid:62) R thu , ∀ u ∈ U . (6)III. T HE OPTIMIZATION FRAMEWORK
In this section, the optimization problem of NOMA clustering for NB-IoT is formulated as a sum rate maximization ofURLLC and mMTC devices. Apart from the QoS constraints in Eq. (2), Eq. (3), Eq. (5), and Eq. (6), we should enforce extraconstraints for the NOMA clustering process. In particular, each URLLC and mMTC device should be assigned to only onecluster with one specific rank, i.e., (cid:88) c ∈C (cid:88) k ∈K α c,km = 1 , ∀ m ∈ M , (7) (cid:88) c ∈C (cid:88) k ∈K β c,ku = 1 , ∀ u ∈ U . (8)Moreover, each rank of one cluster should be assigned either to one URLLC or one mMTC, i.e., (cid:88) m ∈M α c,km + (cid:88) u ∈U β c,ku = 1 , ∀ c ∈ C , ∀ k ∈ K . (9)Since NOMA is to share spectral resources between multiple users, the NOMA clustering enforces existence of more than oneuser in each cluster, i.e., (cid:88) m ∈M (cid:88) k ∈K α c,km + (cid:88) u ∈U (cid:88) k ∈K β c,ku (cid:62) , ∀ c ∈ C . (10)Note that the order of users in each cluster c ∈ C can significantly affect the network throughput. The URLLC devicesare prioritized to have the lowest ranks of clusters (i.e., k = 1 , , ... ) due to their higher data rate and transmission powerrequirements. In other words, the high power of URLLCs do not affect the low power mMTC devices during the SIC process,if they are assigned to the lowest ranks of clusters. Therefore, for the k th ( (cid:54) k (cid:54) k max ) rank of each cluster, the mMTCdevices should always have higher ranks than the URLLC devices, i.e., β c,ku (cid:62) α c,k − m , ∀ m ∈ M , ∀ u ∈ U , ∀ c ∈ C , (11)and we ensure the ranks’ assignment priority in each cluster, by starting rank assignments from the lowest rank of each cluster( k = 1 ), i.e., α c,km (cid:54) α c,k − m , ∀ m ∈ M , ∀ c ∈ C , (cid:54) k (cid:54) k max , (12) β c,ku (cid:54) β c,k − u , ∀ u ∈ U , ∀ c ∈ C , (cid:54) k (cid:54) k max . (13)Finally, the NOMA clustering optimization problem for NB-IoT as a sum rate maximization of URLLC and mMTC devicescan be given as P1: max p sm ,p su ,α c,km ,β c,ku ,γ s,c (cid:88) m ∈M R m + (cid:88) u ∈U R u s.t.C R m (cid:62) R thm , ∀ m ∈ M ,C (cid:88) s ∈S p sm (cid:54) P max m , ∀ m ∈ M ,C R u (cid:62) R thu , ∀ u ∈ U ,C (cid:88) s ∈S p su = P max u , ∀ u ∈ U ,C β c,ku (cid:62) α c,k − m , ∀ m ∈ M , ∀ u ∈ U , ∀ c ∈ C , (cid:54) k (cid:54) k max ,C α c,km (cid:54) α c,k − m , ∀ m ∈ M , ∀ c ∈ C , (cid:54) k (cid:54) k max C β c,ku (cid:54) β c,k − u , ∀ u ∈ U , ∀ c ∈ C , (cid:54) k (cid:54) k max C (cid:88) c ∈C (cid:88) k ∈K α c,km = 1 , ∀ m ∈ M ,C (cid:88) c ∈C (cid:88) k ∈K β c,ku = 1 , ∀ u ∈ U ,C
10 : (cid:88) m ∈M α c,km + (cid:88) u ∈U β c,ku = 1 , ∀ c ∈ C , ∀ k ∈ K ,C
11 : (cid:88) m ∈M (cid:88) k ∈K α c,km + (cid:88) u ∈U (cid:88) k ∈K β c,ku (cid:62) , ∀ c ∈ C ,C
12 : (cid:88) c ∈C γ s,c = 1 , ∀ s ∈ S ,C
13 : (cid:88) s ∈S (cid:88) c ∈C γ s,c W s,c (cid:54) W RB , ∀ c ∈ C , ∀ s ∈ S C
14 : p sm (cid:62) , ∀ m ∈ M , ∀ s ∈ S ,C
15 : p su (cid:62) , ∀ u ∈ U , ∀ s ∈ S ,C
16 : γ s,c ∈ { , } , ∀ c ∈ C , ∀ s ∈ S ,C
17 : α c,km ∈ { , } , ∀ m ∈ M , ∀ c ∈ C , ∀ k ∈ K ,C
18 : β c,ku ∈ { , } , ∀ u ∈ U , ∀ c ∈ C , ∀ k ∈ K , (14)where C1 imposes the data rates of mMTC devices to be greater than the minimum data rate requirement. C2 limits the totaltransmission power of the m th mMTC to the maximum power budget, P maxm . C3 implies that the minimum data rate constraintfor each URLLC device must be satisfied. C4 is the power budget constraint for each URLLC device. C5 is to ensure that theranks of mMTC devices are higher than those of URLLCs for each NOMA cluster. C6 and C7 imply that mMTC and URLLCdevices can be assigned to the k th rank of the c th cluster if all the lower ranks are already allocated to other users. C8 andC9 are designed to guarantee that each device (mMTC and URLLC) is allocated to only one cluster and one specific order within the cluster. C10 specifies that each rank of a cluster cannot be allocated to both mMTC and URLLC devices. C11 is toguarantee each NOMA cluster to have more than one member. C12 implies that each sub-carrier cannot be allocated to morethan one cluster. C13 ensures that the total bandwidth allocated to all NOMA clusters is not more than the bandwidth of oneRB (bandwidth of one RB in NB-IoT is 180 kHz). C14 and C15 are to limit the transmission powers of mMTCs and URLLCsto positive values. C16, C17 and C18 ensure that the variables γ s,c , α c,km , and β c,ku are restricted to binary values, respectively. Lemma 1
The general optimization problem of NOMA clustering problem for NB-IoT in Eq. (14) is an NP-hard problem.Proof:
Without loss of generality, we assume that URLLC and mMTC users are assigned to different clusters with variousranks in the clusters. Therefore, the values of α c,km , and β c,ku are determined and the corresponding constraints in P1 arerelaxed. Given that URLLC and mMTC users transmit their data with predetermined transmission powers of p su and p sm , theconstraints related to these two variables are relaxed and the NOMA clustering optimization problem for NB-IoT as a sum ratemaximization of URLLC and mMTC devices is reduced to the following: P2: max γ s,c (cid:88) s ∈S (cid:88) c ∈C γ s,c (cid:32) (cid:88) m ∈M R s,cm + (cid:88) u ∈U R s,cu (cid:33) s.t.C (cid:88) s ∈S (cid:88) c ∈C γ s,c W s,c (cid:54) W RB , ∀ c ∈ C , ∀ s ∈ S C (cid:88) c ∈C γ s,c = 1 , ∀ c ∈ C , ∀ s ∈ S C γ s,c ∈ { , } , ∀ c ∈ C , ∀ s ∈ S (15)Hence, the reduced optimization problem, P2 , is similar to a Multiple Choice Knapsack Problem (MCKP). In fact, theproblem would be the problem of packing |S| items (sub-channels) into |K| knapsacks (clusters). Each item (sub-channel), s ,has a weight if allocated to the c th knapsack (cluster). Moreover, each sub-channel has a profit which is ( (cid:80) m ∈M R s,cm + (cid:80) u ∈U R s,cu ) and the problem is to choose items such that the profit sum is maximized without exceeding the capacity, W RB . Therefore, P2 is NP-hard because it is categorized as a MCKP which is a generalization of the ordinary knapsack problem. Thus, as P2 is aspecial case of P1 , the general optimization problem in Eq. (14) is an NP-hard problem.The formulated optimization problem is a non convex mixed integer nonlinear programming (MINLP) problem which iscombinatorial, and exploiting exhaustive search presents exponential time complexity. Therefore, we solve the optimizationproblem by proposing a heuristic algorithm. IV. P
ROPOSED A LGORITHM
Algorithm 1
NOMA Clustering and Resource Allocation for Machine Type Communication
Initialization
Input: C , R thm , R thu , P maxm , P maxu , h sm , and h su , ∀ m ∈ M , ∀ u ∈ U , ∀ s ∈ S URLLC Clustering
Sorting URLLC devices ∀ u ∈ U : ˜ h (cid:62) ˜ h (cid:62) ... (cid:62) ˜ h U for all u ∈ U doif U ≤ C do Assign URLLC devices { , , ..., U } to the lowest rank ( k = 1 ) of { , , ..., C } clusters else Assign URLLC { , , ..., C } to the lowest rank of all C clusters, and { C + 1 , C + 2 , ..., U } to the higher ranks end ifend for mMTC Clustering Sorting mMTC devices ∀ m ∈ M : ˜ h (cid:62) ˜ h (cid:62) ... (cid:62) ˜ h M for all k ∈ K doif U < C do Assign mMTC { , ..., ( C − U ) } to the lowest rank ( k = 1 ) of { ( U + 1) , ..., C } clusters. else Assign mMTC { , ..., ( C − U ) } to the next available rank of { ( U + 1) , ..., C } clusters. end ifend for Resource Allocation for NOMA Clusters
Set R u = 0 , R m = 0 , p sm = P maxm and p su = P maxu , ∀ m ∈ M , ∀ u ∈ U , ∀ s ∈ S , ˆ S ← ∅ , S ca ← ∅ , C ns ← C While
S (cid:54) = ∅ and R u < R thu and R m < R thm Select the best cluster c ∗ , ∀ c ∈ C , for each sub-carrier s ∈ S : c ∗ = arg max c ∈ C ns (cid:0)(cid:80) u ∈U R u + (cid:80) m ∈M R m (cid:1) ;Allocate the sub-carrier s to the cluster c ∗ :Set γ s,c ∗ = 1 , and update S c ∗ a ← S c ∗ a ∪ { s } , ˆ S ← ˆ S ∪ { s } Update the rates: R u = R u + R u,s , R m = R m + R m,s Update the powers: URLLC and mMTC of c ∗ individually perform SUWF over all allocated sub-carriers: p sm = p sm | S c ∗ a | +1 , p su = p su | S c ∗ a | +1 , ∀ s ∈ S if R u (cid:62) R thu and R m (cid:62) R thm , ∀ m, u from cluster c ∗ do C ns ← C ns \{ c ∗ } end if S ← S\ ˆ S if R u (cid:62) R thu and R m (cid:62) R thm , ∀ m ∈ M , ∀ u ∈ U dofor all s ∈ S do c ∗ = arg max c ∈ C (cid:0)(cid:80) u ∈U R u + (cid:80) m ∈M R m (cid:1) Set γ s,c ∗ = 1 , S c ∗ a ← S c ∗ a ∪ { s } end for Update p sm = p sm | S c ∗ a | +1 , p su = p su | S c ∗ a | +1 end ifEnd while In this section, we propose an efficient heuristic algorithm to find sub-optimal solutions of the non convex MINLP problemin Eq. (14). The proposed algorithm optimizes the NOMA clustering of mMTC and URLLC devices and allocates spectralresources to the NOMA clusters. The pseudo code for solving the optimization problem is summarized in Algorithm 1. The firstphase of the algorithm is the URLLC clustering, where the URLLC devices are sorted based on their average channel gains, ˜ h u = (cid:80) s ∈S h su / S . As discussed in Subsection ?? , the URLLC devices have higher data rate and transmission power requirements. Therefore, to mitigate the adverse impacts of interference caused by the URLLCs’ high transmission powers, the ranks ofURLLC devices in each cluster should be lower than the mMTC ones. In the URLLC clustering process, URLLC devices withhigher ˜ h u are assigned to the lowest ranks of NOMA clusters, i.e., k = 1 . If the number of URLLC devices, U , is greater thanthe number of NOMA clusters, C , the remaining devices are assigned to the next ranks of clusters. Similar to the URLLCclustering approach, the mMTC clustering procedure is based on the average channel gain of mMTC devices, ˜ h m = (cid:80) s ∈S h sm / S .The mMTC devices with higher ˜ h m are allocated to the next available rank of clusters. Then, the remaining mMTC devicesare allocated to the higher ranks of NOMA clusters. By this NOMA clustering approach, constraints 5-11 in Eq. (14) aretaken into consideration. After the NOMA clustering process, the resource allocation for URLLC and mMTC devices aredetailed in Algorithm 1. The initial values for the transmission rates and powers of URLLC and mMTC devices are R u = 0 , p su = P maxu , and R m = 0 , p sm = P maxm , respectively. The resource allocation phase continues until all the sub-channels areallocated to NOMA clusters and the data rate requirements of mMTC and URLLC devices are satisfied. Denote S ca ← ∅ as theset of allocated sub-channels to the c th cluster, and C ns ← C as the set of clusters of devices with unsatisfied rates. For eachsub-carrier, the best cluster ( c ∗ ) is the one that maximizes the total throughput, i.e., c ∗ = arg max c ∈ C ns (cid:0)(cid:80) u ∈U R u + (cid:80) m ∈M R m (cid:1) .Then, the data rates of the mMTC and URLLC devices and their transmission powers are updated accordingly. Note that eachMTC device performs Single User Water Filling (SUWF) [17] technique over all allocated sub-channels. During the resourceallocation process, clusters with satisfied data rates are excluded from the set of C ns . The algorithm iteratively allocates thesub-channels one by one until all the mMTC and URLLC devices’ rate requirements are met. A. Power Allocation
Given the URLLC and mMTC user allocation to NOMA clusters and spectrum allocation to the clusters, the binary variablesof α c,km , β c,ku and γ s,c in P1 take on 0 or 1. Therefore, all integer constraints are removed and the new optimization problem,which tries to find optimal values of URLLC and mMTC transmission powers, can be expressed as P3: max p sm ,p su (cid:88) m ∈M R m + (cid:88) u ∈U R u s.t.C , C , C , C , C , and C in P1 (16)The reduced optimization problem, given its original formulation in P3 , is apparently non-convex due to the inter-ference users introduce to each other. To address this, we first define a new set of both URLLC and mMTC users, J = { , , ..., U, U + 1 , ..., U + M } for one cluster (the result is also valid for more clusters). Let λ j (cid:44) | h j | N W , where h j is thechannel coefficient from the j th user to the eNB. Without loss of generality, we order users by their normalized channel gains as λ (cid:54) λ (cid:54) ... (cid:54) λ U + M . Note that users exploit SIC at their receivers such that P (cid:62) P (cid:62) ... (cid:62) P U (cid:62) P U +1 (cid:62) ... (cid:62) P U + M ,where P j (cid:44) (cid:80) s ∈S p sj . Therefore, P3 can be rewritten as P4: max P j (cid:88) j ∈J R j s.t.C R j (cid:62) R thj , ∀ j ∈ J ,C (cid:88) j ∈J P j (cid:54) P max , ∀ j ∈ J ,C P (cid:62) P (cid:62) ... (cid:62) P U (cid:62) P U +1 (cid:62) ... (cid:62) P U + M , (17)where R j (cid:44) W RB log (1 + λ j P j λ j (cid:80) U + Ml = j +1 P l ) . To make P4 convex, we use the variable transformations of Z j = (cid:80) U + Ml = j P l , ∀ j ∈J , or P j = Z j − Z j +1 , ∀ j ∈ { , , ..., U + M − } and P U + M = Z U + M . Therefore, we can rewrite R j , ∀ j ∈ { , , ..., U + M − } as R j = log (cid:18) λ j P j λ j (cid:80) U + Ml = j +1 P l (cid:19) = log (cid:18) λ j (cid:80) U + Ml = j P l λ j (cid:80) U + Ml = j +1 P l (cid:19) = log (cid:16) λ j Z j λ j Z j +1 (cid:17) = log (1 + λ j Z j ) − log (1 + λ j Z j +1 ) , (18)while for j = U + M , R U + M = log (1 + λ U + M Z U + M ) . Thus, the objective function in P3 ( (cid:80) U + Mj =1 R j ) can be written as (cid:88) U + M − j =1 W RB [log (1 + λ j Z j ) − log (1 + λ j Z j +1 )]+ W RB log (1 + λ U + M Z U + M ) = (cid:88) U + Mj =1 Φ j ( Z j ) , (19)where Φ ( Z ) (cid:44) W RB log (1 + λ Z ) , and for all j ∈ { , , ..., U + M } , Φ j ( Z j ) (cid:44) W RB [log (1 + λ j Z j ) − log (1 + λ j − Z j )] . (20)The rate constraint, C1 in P4 , can be linearized by using Z j +1 (cid:54) δ j Z j − ρ j for all j ∈ { , , ..., U + M − } , and Z U + M (cid:62) θ U + M , where δ j (cid:44) − R thj , ρ j (cid:44) (1 − δ j ) λ j , and θ j (cid:44) (2 Rthj − λ j . The transmission power in C2 of P4 can be equivalent to Z = (cid:80) U + Mj =1 P j = P max . The power order constraint, C3 in P4 , P (cid:62) P (cid:62) ... (cid:62) P U + M (cid:62) is equivalent to Z − Z (cid:62) Z − Z (cid:62) ... (cid:62) Z U + M (cid:62) . Therefore, the power allocation problem in P4 can be transformed to the following optimizationproblem P5: max Z (cid:88) j ∈J Φ j ( Z j ) s.t.C Z j +1 (cid:54) δ j Z j − ρ j ,C Z = P max ,C Z − Z (cid:62) Z − Z (cid:62) ... (cid:62) Z U + M (cid:62) θ j , (21)where Z (cid:44) ( Z j ) U + Mj =1 . Note that the transformation between P and Z is linear, and therefore the convexity of P3 is equivalent to the convexity of P5 . Theorem 1
Given λ (cid:54) λ (cid:54) ... (cid:54) λ U + M , the power allocation problem in P3 (or equivalently P5 ) is a convex optimizationproblem, for all j ∈ { , , ..., U + M } .Proof: We start to prove the theorem by investigating the objective function of P5 ( Φ j ( Z j ) ) due to the fact that allconstraints are linear. The derivative of the objective function for all j ∈ { , , ..., U + M } is given by Φ j ( Z j ) dZ j = λ j λ j Z j − λ j − λ j − Z j . (22)The second derivative of Φ j ( Z j ) is given by Φ (cid:48)(cid:48) j ( Z j ) = − ( λ j ) (1 + λ j Z j ) − − ( λ j − ) (1 + λ j − Z j ) = λ j − − λ j + 2 λ j Z j λ j − − λ j − Z j λ j (1 + λ j Z j ) (1 + λ j − Z j ) (23)Given λ (cid:54) λ (cid:54) ... (cid:54) λ U + M , the numerator of the second derivative is negative and the denominator is always positive.Therefore, the second derivative is negative and the objective function is concave.V. S IMULATION R ESULTS
In this section, we evaluate the system performance of the proposed NOMA based NB-IoT scheme with sub-carrier andpower allocation, and the NOMA clustering via Monte Carlo simulation. We consider one cell with . km radius where thelocations of the mMTC and URLLC devices are randomly generated and uniformly distributed within the cell. We considerone PRB with 48 sub-carrier spacing of 3.75 kHz for the MTC uplink transmissions in one time slot. We model the channelgains of the mMTC devices as h sm = Y d − βm,s (similarly h su for URLLCs), where Y is a random value generated based on theRayleigh distribution, d − βm,s represents the distance between the transmitter and receiver, and β is the path-loss exponent. Weset β = 3 and d is varied between 0.1 m to 500 m. We also consider Additive White Gaussian Noise (AWGN) with powerspectral density of -173 dBm/Hz. The maximum transmission power budgets of all URLLC and mMTC devices, P maxu and P maxm ( ∀ u ∈ U , ∀ m ∈ M ), are set to 23 dbm. The data rate thresholds of the mMTC devices follow uniform distribution, i.e., R thm = Uniform (0 . , kbps. The bandwidth of each sub-carrier in one PRB with 48 sub-carriers is set to w = 3 . kHz. TheOrthogonal Frequency Division Multiple Access (OFDMA) scheme as an OMA scheme and the fast OFDM [24] approach areused for benchmark comparison.Fig. 2 compares the sum rate of the NOMA and the OMA schemes for an NB-IoT system with respect to the total numberof mMTC and URLLC devices. As we can see in this figure, the performance gain in the total throughput for the proposedNOMA based NB-IoT scheme over the OMA scenario is approximately for a sufficiently large number of users. Owing tothe multi-user diversity gain, the sum rate increases according to the number of users. Note that the ratio of the mMTC devicesto the URLLC ones is set to 3, and the data rate thresholds of the URLLC devices are uniformly distributed between 0.1 kbpsand 20 kbps. Fig. 2. The total throughput of a NOMA based NB-IoT system with respect to the number of users (mMTC and URLLC devices).Fig. 3. The fairness comparison between OMA and NOMA schemes.
To compare the fairness of the proposed NOMA scheme and the OMA scenario, the Jain’s fairness index [17] is adoptedfor data rates of mMTC and URLLC devices, i.e., Fairness Index = ( (cid:80) Uu =1 R u + (cid:80) Mm =1 R m ) ( U + M ) ( (cid:80) Uu =1 R u + (cid:80) Mm =1 R m ) . In fact, Jain’s fairness indexis bounded between 0 and 1, and the maximum value is obtained if all the devices achieve exactly the same throughput.Fig. 3 shows the Jain’s fairness index for both NOMA and OMA schemes. As the figure shows, the NOMA scheme for both k max = 2 and k max = 4 scenarios are fairer as compared to the OMA scheme because the OMA scheme does not allocate onesub-channel to more than one user, thus depriving some users from spectral resources.Fig. 4 compares the performance of the proposed NOMA based NB-IoT with the OMA and the fast OFDM approaches withrespect to the number of the MTC devices with satisfied rate requirements. Note that, the OMA scheme cannot support more Fig. 4. The comparison between NOMA, OMA and fast OFDM in terms of the number of users with satisfied rate requirements. than 48 users as it allocates each sub-carrier of an NB-IoT system to only one user. NOMA outperforms both the fast OFDMand the OFDMA (as an OMA technique), and facilitates a higher number of successfully connected MTC devices.VI. C
ONCLUSION
In this paper, we have proposed a power domain NOMA scheme with user clustering in an NB-IoT system. In particular, theMTC devices are assigned to different ranks within the NOMA clusters where they transmit over the same frequency resources.Then, we have formulated an optimization problem to maximize the total throughput of the network by optimizing the resourceallocation of MTC devices and NOMA clustering while satisfying the transmission power and QoS requirements. We havefurther designed an efficient heuristic algorithm to solve the proposed optimization problem by jointly optimizing NOMAclustering and resource allocation of MTC devices. Finally, we have presented simulation results to validate the efficiency ofour proposal. R
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