Energy-Efficient Uplink Resource Units Scheduling for Ultra-Reliable Communications in NB-IoT Networks

1Department of Computer Science and Information Engineering, Chang Gung University, Kweishan, Taoyuan 33378, Taiwan 2Department of General Medicine, Chang Gung Memorial Hospital, Taoyuan, Taiwan 3Department of Computer Science, National Chiao Tung University, HsinChu 30010, Taiwan 4Department of Electrical Engineering, National University of Tainan, Tainan, Taiwan 5Research Center for Information Technology Innovation, Academia Sinica, Taipei 11574, Taiwan


Introduction
The Internet of Things (IoT) is one of the key applications and technologies in the fifth-generation (5G) communications.Since IoT is widely used for remote monitoring and reporting, such as smart building, smart transportation, smart grid, e-health, and/or factory automation, it makes our life more convenient and makes industry more efficient.Therefore, the 3rd generation partnership project (3GPP) develops a new technology, Narrowband Internet of Things (NB-IoT) [1,2], as the communication standard for IoT, which is featured by low cost, low energy consumption, low complexity, and low throughput.Besides, the NB-IoT supports massive connectivity and enhances the benefit of spectrum reuse.Specifically, it supports multiple types of resource units (RU) with specific repetitions for data transmission to improve the scheduling flexibility and enhance communication reliability.In addition, NB-IoT also provides three-operation modes to flexibly reuse the spectrum of LTE and GSM, which can achieve higher spectrum utilization and reduce the extra deployment cost for the operators.
On the other hand, due to the inherent behaviors of IoT applications, such as remote monitoring and reporting, IoT devices need to operate for a very long time [3].Thus, energy consumption becomes a key issue.Currently, NB-IoT provides discontinuous reception to save devices' energy based on wake-up and sleep operation.However, how to further decrease their transmission energy during wake-up period is an open problem.In addition, the reliability of transmission is also a key issue in QoS for uplink transmission especially for mission critical applications (e.g., e-health, intelligent transport), voice applications, and the high timing precision factory automation [4][5][6].Thus, NB-IoT provides the maximum repetition time up to 128 for a scheduling resource allocation to the ultra-reliability issue.But, how to optimize the repetition operation to achieve high reliability while reducing the waste of resource and energy is still an open issue.
In this paper, we study how to ensure the high transmission reliability to guarantee the strict QoS for devices based on the RU scheduling and repetition determination while minimizing their energy consumption in NB-IoT networks.We first model the problem as an optimization problem and prove it to be NP-complete.Then, we propose an energy-efficient and ultra-reliable heuristic, which consists of two phases.The first phase tries to select the primary parameters which conduct the lowest energy consumption and ensure QoS requirements for uplink transmission.The second phase applies a weighting strategy to determine the precise scheduling order of uplink requests based on the scheduling emergency and inflexibility.In addition, it also adjusts the corresponding results appropriately to satisfy the strict delay constraint if needed while considering energy efficiency.Extensive simulation results show that our scheme can enlarge the number of serving devices with guaranteed QoS and decrease the packet drop ratio while saving energy.
The rest of this paper is organized as follows.Related work is discussed in Section 2. Preliminaries are given in Section 3. Section 4 presents our scheme.Simulation results are shown in Section 5. Section 6 concludes the paper.

Related Work
In the literature, the studies [7,[9][10][11] give an overview of NB-IoT and conclude that NB-IoT can enhance bandwidth efficiency and increase network coverage.Reference [12] proposes a new procedure for cell search and initial synchronization in NB-IoT which can speed up the access operation for the devices with low SNR.In [13], it proposes a new channel equalization algorithm to optimize the sampling rate of devices when NB-IoT and LTE share the same spectrum.However, they neglect the QoS and reliability of transmissions.The research [14] leverages the modulation and coding scheme (MCS) and repetition number to enhance the QoS satisfaction and transmission latency.However, it does not leverage different types of RUs; thus, it will reduce the service coverage of NB-IoT and cannot allocate resource flexibly and effectively.In [15], the authors develop a new detection mechanism for random access procedure to enhance the coverage and access efficiency of NB-IoT.However, it does not consider the transmission reliability and energy efficiency.The study [16] proposes a transmission scheme without connection setup to reduce connectivity latency.But, it may cause extra energy consumption.Reference [17] develops a detection scheme based on maximum likelihood to detect timing acquisition with low delay while reducing energy consumption.However, the QoS satisfaction and the transmission reliability are ignored in this paper.In [18], the authors develop a prediction method to allocate resource in advance based on the occurrence and delay time of uplink transmission.Although it can accelerate the transmission procedure, it may decrease the scheduling flexibility and resource efficiency.In [19], it leverages Nonorthogonal Multiple Access (NOMA) to allocate common subcarriers to multiple devices and thus to enhance the spectrum efficiency.However, it does not discuss how to ensure the energy efficiency and transmission reliability, which are the key issues in NB-IoT.
Based on the above observation, it motivates us to address the issue of considering both transmission reliability and energy efficiency by scheduling multitypes of RUs with optimal repetition in NB-IoT networks.

Preliminary
In this section, we first give an overview of the operation modes of NB-IoT.Then, we introduce the resource unit and the repetition mechanism used in NB-IoT.Finally, we formally define our resource allocation problem and show it to be NP-complete.

NB-IoT Operation Modes.
In NB-IoT, all devices connect with the centralized base station (also called the Evolved Node B, eNB).In order to enhance the spectrum utilization and reduce the cost of operators, NB-IoT provides threeoperation modes for devices to access the eNB by reusing the existing spectrum of LTE and GSM [20][21][22]: Using the bandwidth of one resource block (RB) inside the LTE carrier as the access spectrum is shown in Figure 1(a).

Guard-Band.
Using the bandwidth of one RB in the guard-band of LTE carrier as the access spectrum is shown in Figure 1(b).= 2  , where  ∈ {0 ⋅ ⋅ ⋅ 7}.Thus, each UE can ensure the transmission reliability based on the individual physical status, such as channel quality, path loss, bit-error-rate (BER), and transmission power.Figure 3 shows an example of 5 UEs with different repetition numbers.Note that the transmission finish time of each UE should not violate its delay constraint.

Downlink Control Information (DCI). Downlink Control Information (DCI) is the control message in Narrowband
Physical Downlink Control Channel (NPDCCH), which is responsible for describing the scheduling results for both downlink and uplink transmissions.Each DCI is with the length of 1 ms.When the eNB completes the RU scheduling, each scheduling result will be carried by one DCI to inform the corresponding UE about its uplink transmission with the designate RU type, subcarrier set, allocation time, and the number of repetitions. ( For each UE  's RUs, the amount of data that UE  can carry depends on the modulation and coding scheme MCS  ∈ {0 ⋅ ⋅ ⋅ 10}.Specifically, the bit-error-rate of the data received by the base station relies on the received signal-to-noise ratioSNR dB (); i.e., SNR dB () = 10 log 10 ( P (  ) / sc where (MCS  ) is the data rate of MCS  (bits per subcarrier × slot).To guarantee the transmission reliability   , we have to leverage the number of repetitions  rep and the successful probability of data transmission    ; i.e., where repetitions.Thus, to ensure the reliability requirement   of   , Equation ( 5) is the necessary requirement.
Note that the scheduling results will be carried by the DCI message, which is scheduled at  DCI  (subframe) for each UE  .Thus, it has to satisfy the delay deadline of UE  ; i.e., where  slot  is the number of slots of single RU (two slots constitutes one ms), which depends on the RU type; i.e., Now, we consider the current scheduling subframe is   (ms), the feasible subcarrier set is  (e.g., || = 12 if subcarrier spacing is 15 KHz), and the available earliest subframe for each subcarrier  to allocate resource to devices is   ,  = 1 ⋅ ⋅ ⋅ ||.Our problem asks how to optimize the uplink scheduling results for each UE  ,  = 1 ⋅ ⋅ ⋅ , by determining (1) the type of RUs ( sc  ), (2) the number of RUs ( RU  ), (3) the subcarrier set of RUs ( sc  ), and (4) the allocation start time of RUs ( sc  ) with (5) the number of repetitions ( rep  ), (6) transmit power of UE  (  ), (7) the modulation and coding scheme (MCS  ), and (8) the subframe index of DCI ( DCI  ) to ensure that no two RUs overlap with each other and the QoS parameters including the request data size (  ), delay constraint (  ), and reliability of transmission (  ) are satisfied while the total energy consumption of UEs, denoted as ∑ =1⋅⋅⋅   , is minimized, where Therefore, our problem can be summarized as an optimization-like problem: subject to (1), ( 2), ( 3), (4) ( 5), (6), and (7).Table 4 also summarizes the notations used in this paper.

Theorem 1. The addressed problem is NP-complete.
Proof.To simplify the proof, we consider the case of subcarrier spacing with 3.75 KHz where the UEs use the singletone only and the modulation and coding scheme (MCS) is monotonic.So, the number of repetitions with minimal transmission power to meet required reliability of each UE is unique.Thus, the energy cost of an UE on each parameter list is also uniquely determined.Then, we formulate the resource allocation problem as a decision problem: energy-efficient ultra-reliable scheduling decision (EUSD) problem.Given a NB-IoT network and the UEs with required reliability for uplink transmission, we ask whether or not there exists a set of numbers of repetitions  Rep such that all UEs can conserve the total energy of  to satisfy their uplink transmission with reliability.Then, we show that EUSD problem is NPcomplete.
We first show that the EUSD problem belongs to NP.Given a problem instance and a solution containing the set of repetition numbers it can be verified whether or not the solution is valid in polynomial time.Thus, this part is proved.
We then reduce the multiple-choice knapsack (MCK) problem [25], which is known to be NP-complete, to the EUSD problem.Consider that there are  disjointed classes of objects, where each class  contains N i objects.In each class , every object x i,j has a profit q i,j and a weight u i,j .Besides, there is a knapsack with capacity of .The MCK problem asks whether or not we can select exact one object from each class such that the total object weight is no larger than  and the total object profit is .
We then construct an instance of the EUSD problem as follows.Let  be the number of UEs.Each UE  has N i repetition selections to transmit data to the eNB.When UE  selects the repetition number x i,j , it will conserve energy of q i,j .Note that the conserved energy of an UE with a particular number of repetition is compared to the same UE's number with the most energy cost.Thus, the system should allocate a RU size of u i,j to transmit UE  's data to the eNB.The total frame space is .Our goal is to let all UEs conserve energy of  and satisfy their transmission requirement.We show that the MCK problem has a solution if and only if the EUSD problem has a solution.
Suppose that we have a solution to the EUSD problem, which is a set of repetition parameters  Rep with the conserved . .be a solution to the MCK problem.Then, for each UE  , we select a repetition number such that UE  conserves energy of q i,i and the size of allocated RUs to transmit UE  's data to the eNB is u i,i .In this way, the conserved energy of all UEs will be  and the overall RU size is no larger than .This constitutes a solution to the EUSD problem, thus proving the only if part.

The Proposed Scheme
Since the EUSD problem is NP-complete, finding the optimal solution is impractical due to the time complexity.Thus, we propose a low-complexity, energy-efficient, and high-reliable scheme to tackle this problem.This scheme consists of two phases.The first phase exploits the strategy of "minimal energy cost" to determine the scheduling parameters of UEs.This scheme first quantifies the consumed energy for each UE and then chooses the one with minimal energy cost and reserves the corresponding parameters as the default transmit setting while satisfying the required reliability.The second phase determines the scheduling order based on the "score function" which considers the emergency level of requests and inflexibility of the scheduling transmission.Then, it determines the best resource location of RUs of each UE based on the "potential resource waste" function to enhance the resource utilization.Finally, if the predetermined results violate an UE's delay requirements on scheduling, the scheme will calculate a "cost ratio" to adaptively adjust the RU assignments.The details of the scheme are described as follows.

Phase 1. Minimal Energy Cost.
The goal of the first phase is to determine the default parameters for each UE, including the type of RUs ( sc  ), the number of RUs ( RU  ), the best number of repetitions ( rep  ), and transmit parameters (MCS  and   ), to guarantee QoS and the transmission reliability.These operations are described as follows.
Step 1.For each UE  ,  = 1 ⋅ ⋅ ⋅ , we first calculate the required number of RUs  RU  according to (4) based on the available RU types and MCS selections.Specifically, the required transmit time to carry the amount of data   cannot be greater than the delay requirements.These results are collected as the feasible setting pairs of RU type and MCS setting for each UE  , denoted as set   ; i.e., where  is the index of feasible setting pair of RU type and MCS for each UE  and  slot , is the number of required slots when the RU type is  sc , , which can be obtained by (7).Note that  slot , is divided by 2 because two slots constitute 1 ms, which is the unit of delay constraint   .
Step 2. For each UE  ,  = 1 ⋅ ⋅ ⋅ , consider the feasible RU type and MCS setting pair ( where is derived from (5) which can be derived from (3).
After that we have all the feasible RU type and MCS setting pairs with each of their allowed repetition numbers  rep , .
Step ).In addition, if needed, it can adaptively adjust the transmission parameters of UEs to ensure the delay constraint and enhance spectrum utilization.The detailed steps are depicted as follows.
Step 1.We first define a score function to evaluate the emergency and inflexibility for each UE  with uplink transmission request, i.e., where  1 ∈ [0, 1] and  2 ∈ [0, 1] are the weighting factors of the degrees of the emergency and inflexibility, respectively, that satisfy  1 +  2 = 1.Note that   is the urgent level of UE  's request compared to others; i.e., where    is the remaining time from the scheduling subframe   (or current subframe) to the delay deadline  req  +   of UE  ; i.e.,    = max (( Ĩnf  is the number of RU types that UE  can choose, which is defined by where and Ψ  sc (  ) is the number of choices of RU types for the feasible setting pair   .That means if UE  has fewer choices, its inflexibility is higher and needs to be scheduled earlier.Now, for each UE  ,  = 1 ⋅ ⋅ ⋅ , we calculate its Score  and sort them in descending order.For the UEs without any request, define its score as −∞.Without loss of generality, we use List to represent the sorted sequence of the UEs. Step where Θ( Step 3. Here, we try to change the type of RUs and/or MCSs of UE  by referring   and choose the new triplet that can satisfy the delay deadline while incurring the least extra energy consumption and resource as follows.
First, we define a cost ratioC

𝛼,𝛽 i
to reflect the results of extra consumed energy over the extra required resource space when the original pair of RU type and MCS, denoted as ), changes to the new pair, denoted   as  = (N sc  i , MCS  i , N where the extra consumed energy is Δ Below, we give an example in Figure 4, where there are four scheduled UEs (UE 1 ∼UE 4 ) and one UE (UE 5 ) to be scheduled.The subframe indexes of DCIs for the four scheduled UEs are  DCI

Simulation Results
In this section, we develop a simulator in C++ language to verify the efficiency of the proposed scheme (currently, the well-known simulator, such as ns-3 [26], has not supported NB-IoT model in terms of channels mappings and access procedures.).The parameters of the simulation are shown in Table 5.Specifically, the simulator emulates a base station to serve  = 3000∼30000 UEs.Based on the model of MAR (Mobile Autonomous Reporting) [8], the uplink requests of UEs arrive randomly with the data size of   = 50∼200 bytes according to the Pareto distribution with  = 2.5.In addition, the interarrival time of requests includes 30 minutes (5%), 1 hour (15%), 2 hours (40%), and 1 day (40%), respectively.
In this simulation, we compare our scheme (Ours) with the standard scheme (Spec) [2], Narrowband Link Adaptation scheme (NBLA) [14], random scheduling scheme (Random), and round robin scheme (RR).Specifically, Spec scheme chooses the single-tone for UEs with constant repetition number for simplicity (the numbers are 1 and 2 in the simulation, denoted as Spec(1) and Spec(2)).NBLA can adjust the MCSs and repetition levels iteratively to ensure the transmission quality and delay.Random scheme schedules the UEs in a random order with a random repetition number.RR scheme schedules the UEs in round robin order with the repetition number of 1.Note that the weighting factors of our scheme is  1 = 0.5 and  2 = 0.5.
We consider five performance metrics: (i) system throughput: the total number of data bits received successfully by the eNB during the experiment period; (ii) the number of serving UEs: the average number of UEs that satisfy QoS and reliability; (iii) resource consumption: the frame space allocated to the uplink transmission over the total frame space; (iv) packet drop rate: the number of dropped packets due to violating delay constraint over the total number of packets; (v) energy consumption per UE: the average consumed energy of each served UE.Note that the scheduling interval is 30 ms and the simulator emulates for 24 hours.

System
Throughput.First, we investigate the effects of number of request UEs on system throughput.As shown in Figure 5(a), we can see that when the number of request UEs increases, the system throughput of all scheme increases fast and then slows down due to system saturation.RR, Spec, and Random perform worse because they cannot satisfy UEs' QoS requirement and reliability.Thus, the total number of data bits received successfully by the eNB is few.Specifically, Spec(2) performs slightly better than Spec(1) because it can meet more UEs' reliability due to applying the larger repetition number.NBLA is better than the above schemes because it can adjust MCSs and repetition levels to satisfy QoS and reliability.Note that our scheme outperforms other schemes because it can flexibly adjust RU type and optimize repetition number to satisfy QoS while ensuring transmission reliability.
We also investigate the effects of distribution of request data size on system throughput.As shown in Figure 5(b), similarly, when the request data size increases, the system throughput of most schemes increases and then slows down due to system saturation.RR and Spec(1) decrease fast because their repetition number is 1 and may not satisfy the successful transmission probability due to larger request size.Our scheme is still the best because it can schedule UEs flexibly while ensuring QoS requirement and reliability.
Then, Figure 5(c) shows the impact of the distribution of delay constraints on system throughout.As can be seen, when the distribution of delay constraints increases, the system throughput of most schemes increases slowly.This is because the longer delay constraint can help more UEs to be satisfied until the frame space is exhausted.RR and Spec(1) increase slowly because they fix repetition number by 1 that would limit the successful transmission probability even when the UEs have longer delay constraint.Note that our scheme has the highest throughput because of its flexible scheduling and appropriate parameter setting.
Finally, we investigate the impact of the distribution of required reliability on system throughout.In Figure 5(d), when the distribution of reliability increases, the system throughput of most schemes decreases.The reason is that more UEs with strict reliability make all schemes harder to serve them due to their higher requirements.RR and Spec(1) decrease dramatically because their repetition number is 1 that could not serve most UEs with higher reliability.Note that our scheme still outperforms others.

Number of Serving
UEs.Then, we investigate the effects of number of request UEs on number of serving UEs.As shown in Figure 6(a), similarly, Random performs the worst because it randomly schedules the UEs with a random repetition number; thus, the QoS and reliability of UEs may not be met.Spec and RR perform slightly better than Random scheme because they prefer to choose single-tone with the fixed repetition number for UEs; thus, it could potentially satisfy more UEs with small data request and lower reliability requirement.Spec(2) is better than Spec(1) because a larger repetition number can achieve higher reliability.NBLA is better than the above schemes because it can adjust the repetition levels and MCSs interactively to satisfy the transmission reliability and delay.Note that our scheme outperforms all others because our scheme can optimize the number of repetitions to satisfy the transmission reliability in phase 1 and apply the best configuration pair of RU type and MCS to ensure QoS while enhancing the spectrum utilization in phase 2.
We also investigate the effects of distribution of request data size on number of serving UEs.As shown in Figure 6(b), contrarily, when the request data size increases, the number of serving UEs of all schemes decreases because the UEs with larger request size consume more frame space.RR and Spec(1) decrease fast because their repetition number is fixed by 1 that would not satisfy the UEs with larger request size.Our scheme is the best because it flexibly schedules UEs to satisfy their delay requirement and reliability.
In Figure 6(c), we observe the impact of the distribution of delay constraints on number of serving UEs.As can be seen, when the distribution of delay constraints increases, the number of serving UEs of all schemes increases slowly.This is because the longer delay constraint can make more UEs tolerate allocation time until the frame space is exhausted.RR and Spec(1) increase very slowly because their fixed repetition number (i.e., 1) would limit the transmission probability although the UEs have longer delay time.Note that our scheme has the highest performance because it can well determine the scheduling setting.
Finally, we investigate the impact of the distribution of required reliability on number of serving UEs in Figure 6(d).
We can see that when the distribution of reliability increases, the number of serving UEs of all schemes decreases.The reason is that more UEs with strict reliability will make schemes hardly serve them due to higher requirements.Note that RR and Spec(1) decrease dramatically because they fix the repetition number by 1 that could not serve the UEs with higher reliability requirements.Also note that our scheme still outperforms others even when the reliability requirements become higher.worse because they usually schedule UEs with single-tone so the UEs' RU length may exceed their delay constraint.NBLA performs better than above schemes because it can choose better repetition number to mitigate packets being dropped.Our scheme has the lowest packet drop rate because our scheme can flexibly select multitype RUs and minimize the number of repetitions to guarantee the QoS while avoiding packets being dropped.We also investigate the effects of distribution of request data size on packet drop rate.As shown in Figure 7(b), similarly, when the request data size increases, the packet drop rate of all schemes increases because the larger request size consumes more resources that may exceed the frame space which makes packet being dropped.RR and Spec(1) increase fast because they could not satisfy the UEs with larger request size, which require higher transmission probability.Our scheme is the best because it can schedule UEs according to their delay and reliability requirements.
Then, in Figure 7(c), we investigate the impact of the distribution of delay constraints on packet drop rate.As can be seen, when the distribution of delay constraints increases, the packet drop rate of all schemes decreases gradually.This is because the longer delay constraint can make more packets tolerate the allocation time before delay expires.RR and Spec(1) decrease very slowly because they fix repetition number by 1 so that it would not help packets being transmitted.Note that our scheme has the lowest packet drop rate because it can well determine the scheduling results.
Finally, we investigate the impact of the distribution of required reliability on packet drop rate in Figure 7(d  can be seen, when the distribution of reliability increases, the packet drop rate of all schemes increases.Our scheme still outperforms others even when the reliability requirements are up to 95-99%.

Resource Consumption.
Here, we investigate the effects of number of request UEs on resource consumption.As shown in Figure 8(a), we can see that when the number of request UEs increases, the resource consumption of all schemes increases.Spec(2), Random, and NBLA perform worst because they usually schedule the UEs with multiple number of repetitions and thus consume more resources.Spec(1) and RR have lower resource consumption because they prefer to choose the UEs with single repetition to reduce resource.Note that our scheme needs the least spectrum resource because our scheme exploits a waste function to avoid resource consumption.
Here, we also investigate the effects of distribution of request data size on resource consumption.As shown in Figure 8(b), similarly, when the request data size increases, the resource consumption of most schemes increases slowly.Spec(2), Random, and NBLA waste more resources because they usually schedule the UEs with multiple repetitions and thus consume more resources.Our scheme is still the best because it can schedule UEs flexibly while ensuring QoS requirement and reliability.
Then, in Figure 8(c), we investigate the impact of the distribution of delay constraints on resource consumption.As can be seen, when the distribution of delay constraints increases, the resource consumption of all schemes increases.This is because the longer delay constraint can make more UEs satisfied that may consume more resources.Note that although Spec(1) has the lowest resource consumption, it incurs lower system throughput, lower number of serving UEs, and higher packet drop rate, as compared to ours.Finally, we investigate the impact of the distribution of required reliability on resource consumption, as shown in Figure 8(d).When the distribution of reliability increases, the resource consumption of most schemes increases.Our scheme increases slightly because our scheme can enlarge the repetition number with multiple tone to satisfy the UEs with higher reliability requirement.

Energy Consumption per UE.
Finally, we investigate the effects of the number of request UEs on energy consumption per UE.As shown in Figure 9(a), we can see that the energy consumption per UE of all schemes increases when the number of request UEs increases.This is because the network is saturated and most satisfied UEs are with higher MCS, which require less resource but consume more energy.Random scheme performs the worst because it randomly chooses the number of repetitions that may potentially increase the transmission time, thus consuming more energy.Spec and RR are better than Random scheme because they only serve the UEs with small size request which consumes less energy.NBLA performs slightly better because it can determine the number of repetitions appropriately but neglects to minimize the transmission power.Note that our scheme performs the best because our scheme can choose the best scheduling parameters of RUs with least energy consumption in phase 1 and the cost to reduce energy consumption in phase 2, thus saving energy more efficiently.
In Figure 9(b), we also investigate the effects of distribution of request data size on energy consumption per UE.As can be seen, when the request data size increases, the energy consumption per UE of all schemes increases.Our scheme incurs the lowest energy consumption because it can determine the minimal transmit power and the corresponding RU setting to save energy.
Then, in Figure 9(c), we observe the impact of the distribution of delay constraints on energy consumption per UE.We can see that when the distribution of delay constraints increases, the energy consumption per UE of all schemes increases.Similarly, our scheme still has the lowest energy consumption because it can calculate the best transmit power and exploit the cost ratio to reduce energy consumption.
Finally, we investigate the impact of the distribution of required reliability on energy consumption per UE. Figure 9(d) shows that when the distribution of reliability increases, the energy consumption of most schemes increases.Our scheme still outperforms all other schemes because it can determine the best scheduling parameters based on the required reliability of UEs.

Conclusion
In this paper, we have addressed the problem of energy saving and reliable communications in NB-IoT networks.We first model this problem as an optimization problem and prove it to be NP-complete.Then, we propose an energyefficient and high-reliable scheme which has two phases.The first phase leverages the strategy of minimal energy cost to default scheduling parameters with least consumption.The second phase the weighting score function to balance the emergency and inflexibility of the request transmission and then serve the UEs with least potential resource waste.Simulation results have verified that our scheme can satisfy more UEs with ultra-reliability and QoS requirement while saving their energy.

Figure 3 :
Figure 3: The example of repetitive transmissions.

Figure 4 :
Figure 4: Examples to schedule UE 5 based on the potential resource waste.
() − ()) + and the extra resource space is ΔArea , = (N sc  i × () − N sc * i × ()) + .Then, we choose the new pair  * which incurs the minimal cost ratio; i.e., * = (N sc  i , MCS  i , N rep  i ) = arg min { ,  |  ∈   − }(24)and replace the default parameters byN sc * i = N sc  i , MCS * i = MCS  i ,and N rep * i = N rep  i accordingly.Finally, go back to Step 2 for further allocation.Through the above steps, we can determine each UE  's subcarrier set  sc  , start time  sc  , and the corresponding configurations of MCS  ,  rep  , and   while ensuring the delay deadline and reducing the waste of spectrum resource and energy.

Figure 5 :
Figure 5: Comparisons on the system throughput of all schemes.

Figure 6 :
Figure 6: Comparisons on the number of serving UEs of all schemes.

Figure 8 :
Figure 8: Comparisons on the resource consumption of all schemes.

WirelessFigure 9 :
Figure 9: Comparisons on energy consumption per UE of all schemes.

Table 1 :
[1] types of resource units (RUs) supported in NB-IoT.The resource unit (RU) is the basic transmission resource unit allocated in the bandwidth of 180 KHz.The transmission data can be carried by one or multiple RUs depending on the request size and MCS.Specifically, NB-IoT supports multiple types of RUs based on the subcarrier spacing as shown in Table1.Since the subcarrier spacing of 15 KHz is mandatory in the standard, we focus on it in this paper[1].For the subcarrier spacing of 15 KHz, there are 4 types of RUs that are classified as single- 3.1.3.Stand-Alone.Using the bandwidth of a reframed GSM carrier as the access spectrum is shown in Figure1(c).3.2.Resource Unit (RU).In NB-IoT, the resource is divided into frames, where each frame consists of 10 subframes.The length of a subframe is 1 ms, which is further divided into two slots.For the uplink transmission, data is transmitted through Narrowband Uplink Shared Channel (NPUSCH).tone(1-tone)ormultitone(3-tone, 6-tone, and 12-tone).Each type of RU is with a specific number of subcarriers and time slots, as shown in Figure2.3.3.Repetition Mechanism.In NB-IoT, one of the key features is the repetition mechanism, which is designed to enhance the reliability of transmission and enlarge the network coverage.According to the NB-IoT standard, the transmission RUs of each device i (also called user equipment i (UE  ) in the following) can associate with a specific number of repetition  rep Table 2 shows the main parameters

Table 3 :
Subcarrier indication and the corresponding subcarrier sets.
) =    eNB   /(, eNB) is the received power at base station and   ,  eNB , and (, eNB) are the transmitter gain, receiver gain, and the path loss between UE  and the eNB, respectively; B is the subcarrier bandwidth; i.e., 15 KHz,  0 is the noise power and  is the interference perceived at the eNB.Note that SNR Req dB (MCS  , BER  ) is the SNR threshold to apply MCS  with the measured bit-error-rate (BER  ).According to Table1, the number of required RUs ( RU  ) for each UE  is

Table 4 :
Summary of notations. 's request from the scheduling subframe   (ms) to the delay deadline Waste(,  sc  ) potential waste of UE  with its allocated subcarrier set Ŝ earliest available allocation subframe (ms) of RUs for subcarrier   sc * of all UEs is .By viewing the possible number of repetitions of an UE as a class of objects and the frame as the knapsack, the repetition numbers in  Rep all constitute a solution to the MCK problem.This proves the if part.Conversely, let x 1,1 , x 2,2 , .
can make UE  not only satisfy the required reliability   but also ensure the corresponding transmission power  ,, in the feasible ranges; i.e., MC , , BER ,, ) ≤  max sc , , MCS , ) ∈   ; we calculate the allowed repetition numbers  rep , in which each  rep ,, ∈  rep , and ( sc , , MCS , , BER ,, ) is a function which returns the minimum transmit power for the RU type  sc , , MCS setting MCS , , and target bit-error-rate BER ,, ; i.e.,  ( sc , , MCS , , BER ,, ) = 10 SNR Req dB (MCS , ,BER ,, )/10 3. Based on the results of Steps 1 and 2, we calculate the most energy-saving repetition number  MCS , , BER ,, ) ×  RU , × Then, reform   as a set of triplets ( sc , , MCS , ,  ) from   as the default parameter of UE  , which incurs the minimum energy consumption by (N sc that can incur the least energy consumption and meet the reliability requirement R i of each UE  .4.2.Phase 2. Weighting Based Flexible Scheduling.The goal of the second phase is to optimize the scheduling results of requests from UEs, including the subcarrier set of RUs ( sc  ) and the start time of RUs ( sc i * , for each feasible combination pair ( sc , , MCS , ) ∈   , where  rep * , = arg min  rep ,, ∈ rep ,  ( sc , , MCS , ,  rep ,, ) ,  ( sc , , MCS , ,  rep ,, ) =  ( sc , , * i , MCS * i , N (N sc i,j ,MCS i,j ,N rep * i,j )∈  {E (N sc i,j , MCS i,j , N rep * i,j )} .
2. Before determining the subcarrier set of RUs, we first define a function Waste(,  sc  ) to reflect the potential waste of resource if UE  's RUs are allocated at subcarrier set  sc  ; i.e., + = max{⋅, 0} outputs the value larger than or equal to 0; max ∈ sc  { Ŝ } means the earliest available resource allocation start time of RUs if the subcarrier set is  sc  , where Ŝ = max{  ,  DCI  + 1} is to ensure allocating RU after DCI.Note that (21) sums up the unused resource space before the resource allocation finish time of UE  if UE  's RUs are allocated at  sc  .Then, based on (21), we choose the best subcarrier set  sc *  that makes UE  have the minimal Waste(,  sc  ) without violating its delay deadline; i.e., sc *  ) is the set of available subcarrier sets when default RU type  sc *   = Ŝ  , respectively.Finally, update   =  DCI  + 1 and then remove UE  from List .However, if  sc *  = Ø, it means that current transmission parameter setting is infeasible and then we check whether or not UE  has other feasible triplet in   other than the default parameter.If yes, go to Step 3 for further adjusting.If no, we remove such UE  from List  and go back to Step 2 to schedule the next UE.The above steps are repeated until List  is empty and then terminate this phase.