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

Authors: Jia-Ming Liang; Kun-Ru Wu; Jen-Jee Chen; Pei-Yi Liu; Yu-Chee Tseng
Journal: Wireless Communications and Mobile Computing
 (2018)

---

## Abstract

For 5G wireless communications, the3GPP Narrowband Internet of Things (NB-IoT) is one of the most promising technologies, which provides multiple types ofresource unit (RU) with a special repetition mechanism to improve the scheduling flexibility and enhance the coverage and transmission reliability. Besides, NB-IoT supports different operation modes to reuse the spectrum of LTE and GSM, which can make use of bandwidth more efficiently. The IoT application grows rapidly; however, those massive IoT devices need to operate for a very long time. Thus, the energy consumption becomes a critical issue. Therefore, NB-IoT provides discontinuous reception operation to save devices’ energy. But, how to further reduce the transmission energy while ensuring the required ultra-reliability is still an open issue. In this paper, we study how to guarantee the reliable communication and satisfy thequality of service (QoS) while minimizing the energy consumption for IoT devices. We first model the problem as an optimization problem and prove it to be NP-complete. Then, we propose an energy-efficient, ultra-reliable, and low-complexity scheme, which consists of two phases. The first phase tries to optimize the default transmit configurations of devices which incur the lowest energy consumption and satisfy the QoS requirement. The second phase leverages a weighting strategy to balance the emergency and inflexibility for determining the scheduling order to ensure the delay constraint while maintaining energy efficiency. Extensive simulation results show that our scheme can serve more devices with guaranteed QoS while saving their energy effectively.


---

## Body

## 1. Introduction

TheInternet of Things (IoT) is one of the key applications and technologies in thefifth-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, the3rd 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 ofresource 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 [4–6]. 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 Section2. Preliminaries are given in Section 3. Section 4 presents our scheme. Simulation results are shown in Section 5. Section 6 concludes the paper.


## 2. Related Work

In the literature, the studies [7, 9–11] 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 themodulation 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 leveragesNonorthogonal 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.


## 3. 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.


### 3.1. NB-IoT Operation Modes

In NB-IoT, all devices connect with the centralized base station (also called theEvolved Node B, eNB). In order to enhance the spectrum utilization and reduce the cost of operators, NB-IoT provides three-operation modes for devices to access the eNB by reusing the existing spectrum of LTE and GSM [20–22]:


#### 3.1.1. Inband

Using the bandwidth of oneresource block (RB) inside the LTE carrier as the access spectrum is shown in Figure 1(a).Figure 1
Three-operation modes of NB-IoT.
(a) (b) (c)


#### 3.1.2. Guard-Band

Using the bandwidth of one RB in the guard-band of LTE carrier as the access spectrum is shown in Figure1(b).


#### 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 intoframes, where each frame consists of 10subframes. The length of a subframe is 1 ms, which is further divided into twoslots. For the uplink transmission, data is transmitted throughNarrowband Uplink Shared Channel (NPUSCH). Theresource 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 Table 1. 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 assingle-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 Figure 2.Table 1
The types of resource units (RUs) supported in NB-IoT.
Subcarrier spacing Number of tones (subcarriers) Classification Number of slots 15 KHz 1 single-tone 16  15 KHz 3 multi-tone 8 6 4 12 2  3.75 KHz 1 single-tone 16Figure 2
Multiple types of RUs.


### 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 devicei (also calleduser equipment i(UEi) in the following) can associate with a specific number of repetition Nirep=2l, where l∈{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.Figure 3
The example of repetitive transmissions.


### 3.4. Downlink Control Information (DCI)

Downlink Control Information (DCI) is the control message inNarrowband 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. Table 2 shows the main parameters in DCI (format N0), which is foruplink grant andscheduling in NPUSCH. Specifically, thesubcarrier indication (Iisc) describes the RU type and the correspondingsubcarrier set to locate RUs. Theresource assignment (NiRU) represents the number of allocated continuous RUs for this transmission schedule excluding repetition. Themodulation and coding scheme (MCSi) means which MCS is applied on this RU transmission. Note that NB-IoT supports 11 types of modulation and coding schemes for uplink, which depend on the bit-error-rate and received signal-to-noise ratio (this will be clear later on). Therepetition number (Nirep) represents the number of repetitions for the scheduled RUs. So, the total amount of RUs assigned to UEi is NiRU×Nirep.Table 2
Main parameters of DCI (format N0).
Parameter Value subcarrier indication (Iisc) 0 ~ 63 resource assignment (NiRU) 0 ~ 7 modulation and coding scheme (MCSi) 0 ~ 10 repetition number (Nirep) 2 l,  l∈{0⋯7}Specifically, subcarrier indication (Iisc∈{0~63}) is used for the description of RU types and their subcarrier set, as shown in Table 3. When the subcarrier spacing is 15 KHz, Iisc∈{0~11} represents the fact that the RU type is single-tone and locates at the subcarrier set of Sisc=Iisc. Thus, it has 12 possible locations. When Iisc∈{12~15}, the RU type is 3-tone and locates at Sisc=3(Iisc-12)+{0,1,2}, which has 4 possible locations, i.e., Sisc∈{{0,1,2},{3,4,5},{6,7,8},{9,10,11}}. When Iisc∈{16~17}, it indicates the RU type of 6-tone, which has 2 possible locations, i.e., Sisc∈{{0,1,2,3,4,5},{6,7,8,9,10,11}}. Finally, when Iisc=18, the RU type is 12-tone, which has a unique location, i.e., Sisc={{0,1,2,3,4,5,6,7,8,9,10,11}} and thus Sisc=1.Table 3
Subcarrier indication and the corresponding subcarrier sets.
Subcarrier indication (Iisc) Set of Allocated subcarriers (Sisc) 0–11 I i s c 12–15 3 ( I i s c - 12 ) + { 0,1 , 2 } 16–17 6 ( I i s c - 16 ) + { 0,1 , 2,3 , 4,5 } 18 { 0,1 , 2,3 , 4,5 , 6,7 , 8,9 , 10,11 } 19–63 reserved


### 3.5. Problem Definition

In this paper, we consider an NB-IoT network with a base station (eNB) servingN UEs. Each UEi, i=1⋯N, has an uplink request with data size Di≥0 (bits), required reliability Ri∈0,1, and strict delay constraint di (ms). To guarantee QoS, assume that the arrival time of the UEi’s request is at Tireqth (ms) and then the data must be uploaded to the base station before the delay deadline Tireq+di. For each UEi, the transmit power is denoted as Pi (mW) which is constrained by the maximum transmit power Pimax; i.e.,(1)0≤Pi≤Pimax.When scheduling, eachUEi has to be assigned one type of RUs; Nisc∈{1,3,6,12}; according to the designate subcarrier indication Iisc∈{0~18}; i.e.,(2)Nisc=1,if0≤Iisc≤113,if12≤Iisc≤156,if16≤Iisc≤1712,ifIisc=18.For eachUEi’s RUs, the amount of data that UEi can carry depends on the modulation and coding scheme MCSi∈{0⋯10}. Specifically, the bit-error-rate of the data received by the base station relies on thereceived signal-to-noise ratioSNRdB(i); i.e.,(3)SNRdBi=10log10⁡P~Pi/NiscBN0+I≥SNRdBReqMCSi,BERi,where P~(Pi)=GiGeNBPi/L(i,eNB) is the received power at base station and Gi, GeNB, and L(i,eNB) are the transmitter gain, receiver gain, and the path loss between UEi and the eNB, respectively;B is the subcarrier bandwidth; i.e., 15 KHz, N0 is the noise power and I is the interference perceived at the eNB. Note thatS N R d B R e q ( M C S i , B E R i ) is the SNR threshold to apply MCSi with the measuredbit-error-rate (BERi).According to Table1, the number of required RUs (NiRU) for each UEi is(4)
N
i
R
U
=
D
i
r
M
C
S
i
×
16
,
i
f
N
i
s
c
=
1
D
i
r
M
C
S
i
×
24
,
o
t
h
e
r
w
i
s
e
,where r(MCSi) is the data rate of MCSi (bits per subcarrier × slot). To guarantee the transmission reliability Ri, we have to leverage the number of repetitions Nirep and the successful probability of data transmission Pis; i.e.,(5)1-1-PisNirep≥Ri,where Pis=(1-BERi)Di is the successful probability [23, 24] if data Di is transmitted one time and 1-(1-Pis)Nirep is the successful probability after Nirep repetitions. Thus, to ensure the reliability requirement Ri of Di, Equation (5) is the necessary requirement.Note that the scheduling results will be carried by the DCI message, which is scheduled atTiDCI (subframe) for each UEi. Thus, it has to satisfy the delay deadline of UEi; i.e.,(6)TiDCI+NiRU×Nislot2×Nirep≤Tireq+di,where Nislot is the number of slots of single RU (two slots constitutes one ms), which depends on the RU type; i.e.,(7)Nislot=16,ifNisc=18,ifNisc=34,ifNisc=62,ifNisc=12.Now, we consider the current scheduling subframe isTs (ms), the feasible subcarrier set is K (e.g., K=12 if subcarrier spacing is 15 KHz), and the available earliest subframe for each subcarrier k to allocate resource to devices is Sk,  k=1⋯K. Our problem asks how to optimize the uplink scheduling results for each UEi,i=1⋯N, by determining (1) the type of RUs (Nisc), (2) the number of RUs (NiRU), (3) the subcarrier set of RUs (Sisc), and (4) the allocation start time of RUs (Tisc) with (5) the number of repetitions (Nirep), (6) transmit power of UEi (Pi), (7) the modulation and coding scheme (MCSi), and (8) the subframe index of DCI (TiDCI) to ensure that no two RUs overlap with each other and the QoS parameters including the request data size (Di), delay constraint (di), and reliability of transmission (Ri) are satisfied while the total energy consumption of UEs, denoted as ∑i=1⋯NEi, is minimized, where(8)Ei=Pi×NiRU×Nislot×Nirep.Therefore, our problem can be summarized as an optimization-like problem:(9)minPi,MCSi,NiRU,Iisc,Nirep⁡∑i=1⋯NEi,subject to (1), (2), (3), (4) (5), (6), and (7).Table4 also summarizes the notations used in this paper.Table 4
Summary of notations.
notation definition Nirep number of repetitions ofUEi Iisc subcarrier indication ofUEi NiRU number of RUs ofUEi MCSi modulation and coding scheme ofUEi Sisc set of allocated subcarriers ofUEi Di uplink request ofUEi (bits) Ri required transmission reliability ofUEi di delay constraint ofUEi (ms) Tireq data arrival time ofUEi (ms) Pi transmit power ofUEi Pimax maximum transmit power ofUEi Nisc RU type ofUEi SNRdB(i) received signal-to-noise ratio ofUEi (dB) P~ received power Gi transmitter gain ofUEi GeNB receiver gain ofUEi L(i,eNB) path loss betweenUEi and the eNB B subcarrier bandwidth of the NB-IoT (Hz) No noise power I interference perceived at the eNB BERi bit-error-rate ofUEi SNRdBReq(⋅) SNR threshold (dB) r(MCSi) data rate ofMCSi (bits per subcarrier × slot) Pis successful probability of data transmission ofUEi TiDCI DCI subframe index ofUEi (ms) Ts index of current scheduling subframe (ms) K feasible subcarrier set Sk index of earliest available subframe of subcarrierk Tisc allocation start time of RU ofUEi (ms) Nislot number of slots for a single RU ofUEi  notations of the proposed scheme definition  Ai feasible setting pairs of RU type and MCS ofUEi Scorei score value ofUEi W 1, W2 weighting factors Emi urgent level ofUEi’s request TjR remaining time ofUEj’s request from the scheduling subframe Ts (ms) to the delay deadline Waste(i,Sisc) potential waste ofUEi with its allocated subcarrier set S^k earliest available allocation subframe (ms) of RUs for subcarrierk Sisc∗ best subcarrier ofUEi Ciα,β cost ratio ofUEi ΨNsc() number of choices of RU typesTheorem 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 single-tone 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, theenergy 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 SRep such that all UEs can conserve the total energy of Q to satisfy their uplink transmission with reliability. Then, we show that EUSD problem is NP-complete.
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 themultiple-choice knapsack (MCK) problem [25], which is known to be NP-complete, to the EUSD problem. Consider that there are n disjointed classes of objects, where each class i contains Ni objects. In each class i, every object xi,j has a profit qi,j and a weight ui,j. Besides, there is a knapsack with capacity of U. 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 U and the total object profit is Q.
We then construct an instance of the EUSD problem as follows. Letn be the number of UEs. Each UEi has Ni repetition selections to transmit data to the eNB. When UEi selects the repetition number xi,j, it will conserve energy of qi,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 ui,j to transmit UEi’s data to the eNB. The total frame space is U. Our goal is to let all UEs conserve energy of Q 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 parametersSRep with the conserved energy of RUs. Each UE can choose exact one repetition number and we need to assign each number to each UE to satisfy their transmission reliability. The total size of RUs cannot exceed the frame space U and the conserved energy of all UEs is Q. 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 SRep all constitute a solution to the MCK problem. This proves theif part.
Conversely, letx1,α1, x2,α2,… be a solution to the MCK problem. Then, for each UEi, we select a repetition number such that UEi conserves energy of qi,αi and the size of allocated RUs to transmit UEi’s data to the eNB is ui,αi. In this way, the conserved energy of all UEs will be Q and the overall RU size is no larger than U. This constitutes a solution to the EUSD problem, thus proving theonly if part.


## 3.1. NB-IoT Operation Modes

In NB-IoT, all devices connect with the centralized base station (also called theEvolved Node B, eNB). In order to enhance the spectrum utilization and reduce the cost of operators, NB-IoT provides three-operation modes for devices to access the eNB by reusing the existing spectrum of LTE and GSM [20–22]:


### 3.1.1. Inband

Using the bandwidth of oneresource block (RB) inside the LTE carrier as the access spectrum is shown in Figure 1(a).Figure 1
Three-operation modes of NB-IoT.
(a) (b) (c)


### 3.1.2. Guard-Band

Using the bandwidth of one RB in the guard-band of LTE carrier as the access spectrum is shown in Figure1(b).


### 3.1.3. Stand-Alone

Using the bandwidth of a reframed GSM carrier as the access spectrum is shown in Figure1(c).


## 3.1.1. Inband

Using the bandwidth of oneresource block (RB) inside the LTE carrier as the access spectrum is shown in Figure 1(a).Figure 1
Three-operation modes of NB-IoT.
(a) (b) (c)


## 3.1.2. Guard-Band

Using the bandwidth of one RB in the guard-band of LTE carrier as the access spectrum is shown in Figure1(b).


## 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 intoframes, where each frame consists of 10subframes. The length of a subframe is 1 ms, which is further divided into twoslots. For the uplink transmission, data is transmitted throughNarrowband Uplink Shared Channel (NPUSCH). Theresource 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 Table 1. 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 assingle-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 Figure 2.Table 1
The types of resource units (RUs) supported in NB-IoT.
Subcarrier spacing Number of tones (subcarriers) Classification Number of slots 15 KHz 1 single-tone 16  15 KHz 3 multi-tone 8 6 4 12 2  3.75 KHz 1 single-tone 16Figure 2
Multiple types of RUs.


## 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 devicei (also calleduser equipment i(UEi) in the following) can associate with a specific number of repetition Nirep=2l, where l∈{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.Figure 3
The example of repetitive transmissions.


## 3.4. Downlink Control Information (DCI)

Downlink Control Information (DCI) is the control message inNarrowband 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. Table 2 shows the main parameters in DCI (format N0), which is foruplink grant andscheduling in NPUSCH. Specifically, thesubcarrier indication (Iisc) describes the RU type and the correspondingsubcarrier set to locate RUs. Theresource assignment (NiRU) represents the number of allocated continuous RUs for this transmission schedule excluding repetition. Themodulation and coding scheme (MCSi) means which MCS is applied on this RU transmission. Note that NB-IoT supports 11 types of modulation and coding schemes for uplink, which depend on the bit-error-rate and received signal-to-noise ratio (this will be clear later on). Therepetition number (Nirep) represents the number of repetitions for the scheduled RUs. So, the total amount of RUs assigned to UEi is NiRU×Nirep.Table 2
Main parameters of DCI (format N0).
Parameter Value subcarrier indication (Iisc) 0 ~ 63 resource assignment (NiRU) 0 ~ 7 modulation and coding scheme (MCSi) 0 ~ 10 repetition number (Nirep) 2 l,  l∈{0⋯7}Specifically, subcarrier indication (Iisc∈{0~63}) is used for the description of RU types and their subcarrier set, as shown in Table 3. When the subcarrier spacing is 15 KHz, Iisc∈{0~11} represents the fact that the RU type is single-tone and locates at the subcarrier set of Sisc=Iisc. Thus, it has 12 possible locations. When Iisc∈{12~15}, the RU type is 3-tone and locates at Sisc=3(Iisc-12)+{0,1,2}, which has 4 possible locations, i.e., Sisc∈{{0,1,2},{3,4,5},{6,7,8},{9,10,11}}. When Iisc∈{16~17}, it indicates the RU type of 6-tone, which has 2 possible locations, i.e., Sisc∈{{0,1,2,3,4,5},{6,7,8,9,10,11}}. Finally, when Iisc=18, the RU type is 12-tone, which has a unique location, i.e., Sisc={{0,1,2,3,4,5,6,7,8,9,10,11}} and thus Sisc=1.Table 3
Subcarrier indication and the corresponding subcarrier sets.
Subcarrier indication (Iisc) Set of Allocated subcarriers (Sisc) 0–11 I i s c 12–15 3 ( I i s c - 12 ) + { 0,1 , 2 } 16–17 6 ( I i s c - 16 ) + { 0,1 , 2,3 , 4,5 } 18 { 0,1 , 2,3 , 4,5 , 6,7 , 8,9 , 10,11 } 19–63 reserved


## 3.5. Problem Definition

In this paper, we consider an NB-IoT network with a base station (eNB) servingN UEs. Each UEi, i=1⋯N, has an uplink request with data size Di≥0 (bits), required reliability Ri∈0,1, and strict delay constraint di (ms). To guarantee QoS, assume that the arrival time of the UEi’s request is at Tireqth (ms) and then the data must be uploaded to the base station before the delay deadline Tireq+di. For each UEi, the transmit power is denoted as Pi (mW) which is constrained by the maximum transmit power Pimax; i.e.,(1)0≤Pi≤Pimax.When scheduling, eachUEi has to be assigned one type of RUs; Nisc∈{1,3,6,12}; according to the designate subcarrier indication Iisc∈{0~18}; i.e.,(2)Nisc=1,if0≤Iisc≤113,if12≤Iisc≤156,if16≤Iisc≤1712,ifIisc=18.For eachUEi’s RUs, the amount of data that UEi can carry depends on the modulation and coding scheme MCSi∈{0⋯10}. Specifically, the bit-error-rate of the data received by the base station relies on thereceived signal-to-noise ratioSNRdB(i); i.e.,(3)SNRdBi=10log10⁡P~Pi/NiscBN0+I≥SNRdBReqMCSi,BERi,where P~(Pi)=GiGeNBPi/L(i,eNB) is the received power at base station and Gi, GeNB, and L(i,eNB) are the transmitter gain, receiver gain, and the path loss between UEi and the eNB, respectively;B is the subcarrier bandwidth; i.e., 15 KHz, N0 is the noise power and I is the interference perceived at the eNB. Note thatS N R d B R e q ( M C S i , B E R i ) is the SNR threshold to apply MCSi with the measuredbit-error-rate (BERi).According to Table1, the number of required RUs (NiRU) for each UEi is(4)
N
i
R
U
=
D
i
r
M
C
S
i
×
16
,
i
f
N
i
s
c
=
1
D
i
r
M
C
S
i
×
24
,
o
t
h
e
r
w
i
s
e
,where r(MCSi) is the data rate of MCSi (bits per subcarrier × slot). To guarantee the transmission reliability Ri, we have to leverage the number of repetitions Nirep and the successful probability of data transmission Pis; i.e.,(5)1-1-PisNirep≥Ri,where Pis=(1-BERi)Di is the successful probability [23, 24] if data Di is transmitted one time and 1-(1-Pis)Nirep is the successful probability after Nirep repetitions. Thus, to ensure the reliability requirement Ri of Di, Equation (5) is the necessary requirement.Note that the scheduling results will be carried by the DCI message, which is scheduled atTiDCI (subframe) for each UEi. Thus, it has to satisfy the delay deadline of UEi; i.e.,(6)TiDCI+NiRU×Nislot2×Nirep≤Tireq+di,where Nislot is the number of slots of single RU (two slots constitutes one ms), which depends on the RU type; i.e.,(7)Nislot=16,ifNisc=18,ifNisc=34,ifNisc=62,ifNisc=12.Now, we consider the current scheduling subframe isTs (ms), the feasible subcarrier set is K (e.g., K=12 if subcarrier spacing is 15 KHz), and the available earliest subframe for each subcarrier k to allocate resource to devices is Sk,  k=1⋯K. Our problem asks how to optimize the uplink scheduling results for each UEi,i=1⋯N, by determining (1) the type of RUs (Nisc), (2) the number of RUs (NiRU), (3) the subcarrier set of RUs (Sisc), and (4) the allocation start time of RUs (Tisc) with (5) the number of repetitions (Nirep), (6) transmit power of UEi (Pi), (7) the modulation and coding scheme (MCSi), and (8) the subframe index of DCI (TiDCI) to ensure that no two RUs overlap with each other and the QoS parameters including the request data size (Di), delay constraint (di), and reliability of transmission (Ri) are satisfied while the total energy consumption of UEs, denoted as ∑i=1⋯NEi, is minimized, where(8)Ei=Pi×NiRU×Nislot×Nirep.Therefore, our problem can be summarized as an optimization-like problem:(9)minPi,MCSi,NiRU,Iisc,Nirep⁡∑i=1⋯NEi,subject to (1), (2), (3), (4) (5), (6), and (7).Table4 also summarizes the notations used in this paper.Table 4
Summary of notations.
notation definition Nirep number of repetitions ofUEi Iisc subcarrier indication ofUEi NiRU number of RUs ofUEi MCSi modulation and coding scheme ofUEi Sisc set of allocated subcarriers ofUEi Di uplink request ofUEi (bits) Ri required transmission reliability ofUEi di delay constraint ofUEi (ms) Tireq data arrival time ofUEi (ms) Pi transmit power ofUEi Pimax maximum transmit power ofUEi Nisc RU type ofUEi SNRdB(i) received signal-to-noise ratio ofUEi (dB) P~ received power Gi transmitter gain ofUEi GeNB receiver gain ofUEi L(i,eNB) path loss betweenUEi and the eNB B subcarrier bandwidth of the NB-IoT (Hz) No noise power I interference perceived at the eNB BERi bit-error-rate ofUEi SNRdBReq(⋅) SNR threshold (dB) r(MCSi) data rate ofMCSi (bits per subcarrier × slot) Pis successful probability of data transmission ofUEi TiDCI DCI subframe index ofUEi (ms) Ts index of current scheduling subframe (ms) K feasible subcarrier set Sk index of earliest available subframe of subcarrierk Tisc allocation start time of RU ofUEi (ms) Nislot number of slots for a single RU ofUEi  notations of the proposed scheme definition  Ai feasible setting pairs of RU type and MCS ofUEi Scorei score value ofUEi W 1, W2 weighting factors Emi urgent level ofUEi’s request TjR remaining time ofUEj’s request from the scheduling subframe Ts (ms) to the delay deadline Waste(i,Sisc) potential waste ofUEi with its allocated subcarrier set S^k earliest available allocation subframe (ms) of RUs for subcarrierk Sisc∗ best subcarrier ofUEi Ciα,β cost ratio ofUEi ΨNsc() number of choices of RU typesTheorem 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 single-tone 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, theenergy 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 SRep such that all UEs can conserve the total energy of Q to satisfy their uplink transmission with reliability. Then, we show that EUSD problem is NP-complete.
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 themultiple-choice knapsack (MCK) problem [25], which is known to be NP-complete, to the EUSD problem. Consider that there are n disjointed classes of objects, where each class i contains Ni objects. In each class i, every object xi,j has a profit qi,j and a weight ui,j. Besides, there is a knapsack with capacity of U. 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 U and the total object profit is Q.
We then construct an instance of the EUSD problem as follows. Letn be the number of UEs. Each UEi has Ni repetition selections to transmit data to the eNB. When UEi selects the repetition number xi,j, it will conserve energy of qi,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 ui,j to transmit UEi’s data to the eNB. The total frame space is U. Our goal is to let all UEs conserve energy of Q 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 parametersSRep with the conserved energy of RUs. Each UE can choose exact one repetition number and we need to assign each number to each UE to satisfy their transmission reliability. The total size of RUs cannot exceed the frame space U and the conserved energy of all UEs is Q. 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 SRep all constitute a solution to the MCK problem. This proves theif part.
Conversely, letx1,α1, x2,α2,… be a solution to the MCK problem. Then, for each UEi, we select a repetition number such that UEi conserves energy of qi,αi and the size of allocated RUs to transmit UEi’s data to the eNB is ui,αi. In this way, the conserved energy of all UEs will be Q and the overall RU size is no larger than U. This constitutes a solution to the EUSD problem, thus proving theonly if part.


## 4. 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.


### 4.1. 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 (Nisc), the number of RUs (NiRU), the best number of repetitions (Nirep), and transmit parameters (MCSi and Pi), to guarantee QoS and the transmission reliability. These operations are described as follows.Step 1.
For eachUEi,i=1⋯N, we first calculate the required number of RUs NiRU according to (4) based on the available RU types and MCS selections. Specifically, the required transmit time to carry the amount of data Di cannot be greater than the delay requirements. These results are collected as the feasible setting pairs of RU type and MCS setting for each UEi, denoted as set Ai; i.e.,(10)Ai=Ni,jsc,MCSi,j∣Ni,jRU×Ni,jslot2≤di,Ni,jsc∈1,3,6,12,MCSi,j∈0⋯10,where j is the index of feasible setting pair of RU type and MCS for each UEi and Ni,jslot is the number of required slots when the RU type is Ni,jsc, which can be obtained by (7). Note that Ni,jslot is divided by 2 because two slots constitute 1 ms, which is the unit of delay constraint di.Step 2.
For eachUEi,i=1⋯N, consider the feasible RU type and MCS setting pair (Ni,jsc,MCSi,j)∈Ai; we calculate the allowed repetition numbers Ni,jrep in which each Ni,j,krep∈Ni,jrep can make UEi not only satisfy the required reliability Ri but also ensure the corresponding transmission power Pi,j,k in the feasible ranges; i.e.,(11)Ni,jrep=Ni,j,krep∣1-1-Pi,j,ksNi,j,krep≥Ri,Ni,j,krep∈2l∣l∈0⋯7,Ni,jRU×Ni,jslot2×Ni,j,krep≤di,0≤PNi,jsc,MCSi,j,BERi,j,k≤Pimax,where(12)BERi,j,k=1-1-1-Ri1/Ni,j,krep1/Diis derived from (5) and P(Ni,jsc,MCSi,j,BERi,j,k) is a function which returns the minimum transmit power for the RU type Ni,jsc, MCS setting MCSi,j, and target bit-error-rate BERi,j,k; i.e.,(13)PNi,jsc,MCSi,j,BERi,j,k=10SNRdBReqMCSi,j,BERi,j,k/10×BN0+I·Li,eNB·Ni,jscGiGeNB,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 numbersNi,jrep.Step 3.
Based on the results of Steps 1 and 2, we calculate the most energy-saving repetition numberNi,jrep∗ for each feasible combination pair (Ni,jsc,MCSi,j)∈Ai, where(14)Ni,jrep∗=arg⁡minNi,j,krep∈Ni,jrep⁡ENi,jsc,MCSi,j,Ni,j,krep,ENi,jsc,MCSi,j,Ni,j,krep=PNi,jsc,MCSi,j,BERi,j,k×Ni,jRU×Ni,jslot2×Ni,j,krep.Then, reformAi as a set of triplets (Ni,jsc,MCSi,j,Ni,jrep∗). Each triplet in Ai is a feasible configuration of RU type, MCS setting, and repetition number.Step 4.
Then, we choose the best triplet of(Nisc∗,MCSi∗,Nirep∗) from Ai as the default parameter of UEi, which incurs the minimum energy consumption by (15)Nisc∗,MCSi∗,Nirep∗=arg⁡minNi,jsc,MCSi,j,Ni,jrep∗∈Ai⁡ENi,jsc,MCSi,j,Ni,jrep∗.Through the above steps, we can determine the best RU typeNisc∗, MCS setting MCSi∗, and repetition number Nirep∗ that can incur the least energy consumption and meet the reliability requirement Ri of each UEi.


### 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 (Sisc) and the start time of RUs (Tisc). 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 ascore function to evaluate the emergency and inflexibility for each UEi with uplink transmission request, i.e.,(16)Scorei=W1×Emi+W2×Infi~,where W1∈0,1 and W2∈0,1 are the weighting factors of the degrees of the emergency and inflexibility, respectively, that satisfy W1+W2=1. Note that Emi is the urgent level of UEi’s request compared to others; i.e.,(17)Emi=maxj⁡TjR-TiRmaxj⁡TjR-minj⁡TjR,where TjR is the remaining time from the scheduling subframe TS (or current subframe) to the delay deadline Tjreq+dj of UEj; i.e.,(18)TiR=max⁡Tireq+di-Ts,0.
I n f i ~ is the number of RU types that UEi can choose, which is defined by(19)Infi~=Infimaxj⁡Infj,where(20)Infi=4,ifΨNscAi=13,ifΨNscAi=22,ifΨNscAi=31,ifΨNscAi>3and ΨNsc(Ai) is the number of choices of RU types for the feasible setting pair Ai. That means if UEi has fewer choices, its inflexibility is higher and needs to be scheduled earlier.
Now, for eachUEi,i=1⋯N, we calculate its Scorei and sort them in descending order. For the UEs without any request, define its score as -∞. Without loss of generality, we useListL to represent the sorted sequence of the UEs.Step 2.
Before determining the subcarrier set of RUs, we first define a functionWaste(i,Sisc) to reflect the potential waste of resource if UEi’s RUs are allocated at subcarrier set Sisc; i.e., (21)Wastei,Sisc=∑k′∈K-Siscmaxk∈SiscS^k+NiRU×Nislot2×Nirep-S^k′++∑k∈Siscmaxk∈SiscS^k-S^k,where (·)+=max⁡{·,0} outputs the value larger than or equal to 0; maxk∈Sisc{S^k} means the earliest available resource allocation start time of RUs if the subcarrier set is Sisc, where S^k=max⁡{Sk,TiDCI+1} is to ensure allocating RU after DCI. Note that (21) sums up the unused resource space before the resource allocation finish time of UEi if UEi’s RUs are allocated at Sisc.
Then, based on (21), we choose the best subcarrier set Sisc∗ that makes UEi have the minimal Waste(i,Sisc) without violating its delay deadline; i.e.,(22)Sisc∗=argminSisc⊆ΘNisc∗Wastei,Sisc∣maxk∈SiscS^k+NiRU∗×Nislot∗2×Nirep∗<Tireq+di,where Θ(Nisc∗) is the set of available subcarrier sets when default RU type Nisc∗ is used.
IfSisc∗≠ Ø, we set the subframe index of DCIi by TiDCI=Ts and start time Tisc=maxk∈Sisc∗S^k. Then, update the available scheduling subframe for subcarriers k∈Sisc∗ and k′∈Θ(Nisc∗)-Sisc∗ by Sk=max⁡maxk∈Sisc∗⁡{S^k}+(NiRU∗×(Nislot∗/2)×Nirep∗),TiDCI+1 and Sk′=S^k′, respectively. Finally, update Ts=TiDCI+1 and then remove UEi from List L. However, if Sisc∗=Ø, it means that current transmission parameter setting is infeasible and then we check whether or not UEi has other feasible triplet in Ai other than the default parameter. If yes, go to Step 3 for further adjusting. If no, we remove such UEi from List L and go back to Step 2 to schedule the next UE. The above steps are repeated until List L is empty and then terminate this phase.Step 3.
Here, we try to change the type of RUs and/or MCSs ofUEi by referring Ai 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 acost ratioCiα,β 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 α=(Nisc∗,MCSi∗,Nirep∗), changes to the new pair, denoted as β=(Nisc′,MCSi′,Nirep′) for (Nisc′,MCSi′,Nirep′)∈Ai-(Nisc∗,MCSi∗,Nirep∗); i.e.,(23)Ciα,β=ΔEiα,βΔAreaiα,β,ifΔAreaiα,β>0ΔEiα,β,ifΔAreaiα,β=0,where the extra consumed energy is ΔEiα,β=(E(β)-E(α))+ and the extra resource space is ΔAreaiα,β=(Nisc′×T(β)-Nisc∗×T(α))+.
Then, we choose the new pairβ∗ which incurs the minimal cost ratio; i.e.,(24)β∗=Nisc′,MCSi′,Nirep′=argmin⁡Ciα,β∣β∈Ai-αand replace the default parameters by Nisc∗=Nisc′, MCSi∗=MCSi′, and Nirep∗=Nirep′ accordingly. Finally, go back to Step 2 for further allocation.Through the above steps, we can determine eachUEi’s subcarrier set Sisc, start time Tisc, and the corresponding configurations of MCSi, Nirep, and Pi while ensuring the delay deadline and reducing the waste of spectrum resource and energy.Below, we give an example in Figure4, where there are four scheduled UEs (UE1~UE4) and one UE (UE5) to be scheduled. The subframe indexes of DCIs for the four scheduled UEs are T1DCI=10, T2DCI=11, T3DCI=12, and T4DCI=13 (ms), separately. The current earliest subframe index for DCI is subframe 14 and scheduling subframe is Ts=14 (ms). Now, we consider schedule UE5, whose RU type is 3-tone, number of RUs is N5RU=1, total length is N5RU×(N5slot/2)=1×(8/2)=4 (ms), arrival time is T5req=4 (ms), and delay constraint is d5=20 (ms). From the current scheduling results, as shown in Figure 4(a), the available start time for each subcarrier is S0=19, S1=19, S2=19, S3=15, S4=15, S5=15, S6=16, S7=16, S8=16, S9=14, S10=14, and S11=21, respectively. Thus, the available subcarrier set for UE5 is S5sc∈{{0,1,2},{3,4,5},{6,7,8},{9,10,11}}. So, for the 4 possible subcarrier sets, the potential resource waste for UE5 is Waste(5,{0,1,2})=∑k′=3~11(max⁡{19,19,19}+1×(8/2)×1)+-S^k′=63, Waste(5,{3,4,5})=∑k′=0~2,6~11(max⁡{15,15,15}+1×(8/2)×1)+-S^k′=17, Waste(5,{6,7,8})=∑k′=0~5,9~11(max⁡{16,16,16}+1×(8/2)×1)+-S^k′=28, and Waste(5,{9,10,11})=∑k′=0~8(max⁡{15,15,21}+1×(8/2)×1)+-S^k′=87, which are the doted regions in Figures 4(b), 4(c), 4(d), and 4(e), respectively. Moreover, the subcarrier set of {9,10,11} in Figure 4(e) is infeasible because it violates the delay deadline of UE5 (i.e., maxk∈{9,10,11}S^k+(N5RU×(N5slot/2)×N5rep)=21+1×(8/2)×1=25≥(T5req+d5)=4+20=24). Thus, based on (21), the scheme chooses the best feasible subcarrier set S5sc∗={3,4,5} and the start time of UE5’s schedules RUs is T5sc=maxk∈{3,4,5}{S^k}=15 because it has the minimal value of Waste(5,{3,4,5})=17.Figure 4
Examples to scheduleUE5 based on the potential resource waste.
(a)
The scheduling results before schedulingUE5 (b)
The scheduling results if subcarrier set is{0,1,2} (c)
The scheduling results if subcarrier set is{3,4,5} (d)
The scheduling results if subcarrier set is{6,7,8} (e)
The scheduling results if subcarrier set is{9,10,11}


## 4.1. 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 (Nisc), the number of RUs (NiRU), the best number of repetitions (Nirep), and transmit parameters (MCSi and Pi), to guarantee QoS and the transmission reliability. These operations are described as follows.Step 1.
For eachUEi,i=1⋯N, we first calculate the required number of RUs NiRU according to (4) based on the available RU types and MCS selections. Specifically, the required transmit time to carry the amount of data Di cannot be greater than the delay requirements. These results are collected as the feasible setting pairs of RU type and MCS setting for each UEi, denoted as set Ai; i.e.,(10)Ai=Ni,jsc,MCSi,j∣Ni,jRU×Ni,jslot2≤di,Ni,jsc∈1,3,6,12,MCSi,j∈0⋯10,where j is the index of feasible setting pair of RU type and MCS for each UEi and Ni,jslot is the number of required slots when the RU type is Ni,jsc, which can be obtained by (7). Note that Ni,jslot is divided by 2 because two slots constitute 1 ms, which is the unit of delay constraint di.Step 2.
For eachUEi,i=1⋯N, consider the feasible RU type and MCS setting pair (Ni,jsc,MCSi,j)∈Ai; we calculate the allowed repetition numbers Ni,jrep in which each Ni,j,krep∈Ni,jrep can make UEi not only satisfy the required reliability Ri but also ensure the corresponding transmission power Pi,j,k in the feasible ranges; i.e.,(11)Ni,jrep=Ni,j,krep∣1-1-Pi,j,ksNi,j,krep≥Ri,Ni,j,krep∈2l∣l∈0⋯7,Ni,jRU×Ni,jslot2×Ni,j,krep≤di,0≤PNi,jsc,MCSi,j,BERi,j,k≤Pimax,where(12)BERi,j,k=1-1-1-Ri1/Ni,j,krep1/Diis derived from (5) and P(Ni,jsc,MCSi,j,BERi,j,k) is a function which returns the minimum transmit power for the RU type Ni,jsc, MCS setting MCSi,j, and target bit-error-rate BERi,j,k; i.e.,(13)PNi,jsc,MCSi,j,BERi,j,k=10SNRdBReqMCSi,j,BERi,j,k/10×BN0+I·Li,eNB·Ni,jscGiGeNB,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 numbersNi,jrep.Step 3.
Based on the results of Steps 1 and 2, we calculate the most energy-saving repetition numberNi,jrep∗ for each feasible combination pair (Ni,jsc,MCSi,j)∈Ai, where(14)Ni,jrep∗=arg⁡minNi,j,krep∈Ni,jrep⁡ENi,jsc,MCSi,j,Ni,j,krep,ENi,jsc,MCSi,j,Ni,j,krep=PNi,jsc,MCSi,j,BERi,j,k×Ni,jRU×Ni,jslot2×Ni,j,krep.Then, reformAi as a set of triplets (Ni,jsc,MCSi,j,Ni,jrep∗). Each triplet in Ai is a feasible configuration of RU type, MCS setting, and repetition number.Step 4.
Then, we choose the best triplet of(Nisc∗,MCSi∗,Nirep∗) from Ai as the default parameter of UEi, which incurs the minimum energy consumption by (15)Nisc∗,MCSi∗,Nirep∗=arg⁡minNi,jsc,MCSi,j,Ni,jrep∗∈Ai⁡ENi,jsc,MCSi,j,Ni,jrep∗.Through the above steps, we can determine the best RU typeNisc∗, MCS setting MCSi∗, and repetition number Nirep∗ that can incur the least energy consumption and meet the reliability requirement Ri of each UEi.


## 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 (Sisc) and the start time of RUs (Tisc). 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 ascore function to evaluate the emergency and inflexibility for each UEi with uplink transmission request, i.e.,(16)Scorei=W1×Emi+W2×Infi~,where W1∈0,1 and W2∈0,1 are the weighting factors of the degrees of the emergency and inflexibility, respectively, that satisfy W1+W2=1. Note that Emi is the urgent level of UEi’s request compared to others; i.e.,(17)Emi=maxj⁡TjR-TiRmaxj⁡TjR-minj⁡TjR,where TjR is the remaining time from the scheduling subframe TS (or current subframe) to the delay deadline Tjreq+dj of UEj; i.e.,(18)TiR=max⁡Tireq+di-Ts,0.
I n f i ~ is the number of RU types that UEi can choose, which is defined by(19)Infi~=Infimaxj⁡Infj,where(20)Infi=4,ifΨNscAi=13,ifΨNscAi=22,ifΨNscAi=31,ifΨNscAi>3and ΨNsc(Ai) is the number of choices of RU types for the feasible setting pair Ai. That means if UEi has fewer choices, its inflexibility is higher and needs to be scheduled earlier.
Now, for eachUEi,i=1⋯N, we calculate its Scorei and sort them in descending order. For the UEs without any request, define its score as -∞. Without loss of generality, we useListL to represent the sorted sequence of the UEs.Step 2.
Before determining the subcarrier set of RUs, we first define a functionWaste(i,Sisc) to reflect the potential waste of resource if UEi’s RUs are allocated at subcarrier set Sisc; i.e., (21)Wastei,Sisc=∑k′∈K-Siscmaxk∈SiscS^k+NiRU×Nislot2×Nirep-S^k′++∑k∈Siscmaxk∈SiscS^k-S^k,where (·)+=max⁡{·,0} outputs the value larger than or equal to 0; maxk∈Sisc{S^k} means the earliest available resource allocation start time of RUs if the subcarrier set is Sisc, where S^k=max⁡{Sk,TiDCI+1} is to ensure allocating RU after DCI. Note that (21) sums up the unused resource space before the resource allocation finish time of UEi if UEi’s RUs are allocated at Sisc.
Then, based on (21), we choose the best subcarrier set Sisc∗ that makes UEi have the minimal Waste(i,Sisc) without violating its delay deadline; i.e.,(22)Sisc∗=argminSisc⊆ΘNisc∗Wastei,Sisc∣maxk∈SiscS^k+NiRU∗×Nislot∗2×Nirep∗<Tireq+di,where Θ(Nisc∗) is the set of available subcarrier sets when default RU type Nisc∗ is used.
IfSisc∗≠ Ø, we set the subframe index of DCIi by TiDCI=Ts and start time Tisc=maxk∈Sisc∗S^k. Then, update the available scheduling subframe for subcarriers k∈Sisc∗ and k′∈Θ(Nisc∗)-Sisc∗ by Sk=max⁡maxk∈Sisc∗⁡{S^k}+(NiRU∗×(Nislot∗/2)×Nirep∗),TiDCI+1 and Sk′=S^k′, respectively. Finally, update Ts=TiDCI+1 and then remove UEi from List L. However, if Sisc∗=Ø, it means that current transmission parameter setting is infeasible and then we check whether or not UEi has other feasible triplet in Ai other than the default parameter. If yes, go to Step 3 for further adjusting. If no, we remove such UEi from List L and go back to Step 2 to schedule the next UE. The above steps are repeated until List L is empty and then terminate this phase.Step 3.
Here, we try to change the type of RUs and/or MCSs ofUEi by referring Ai 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 acost ratioCiα,β 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 α=(Nisc∗,MCSi∗,Nirep∗), changes to the new pair, denoted as β=(Nisc′,MCSi′,Nirep′) for (Nisc′,MCSi′,Nirep′)∈Ai-(Nisc∗,MCSi∗,Nirep∗); i.e.,(23)Ciα,β=ΔEiα,βΔAreaiα,β,ifΔAreaiα,β>0ΔEiα,β,ifΔAreaiα,β=0,where the extra consumed energy is ΔEiα,β=(E(β)-E(α))+ and the extra resource space is ΔAreaiα,β=(Nisc′×T(β)-Nisc∗×T(α))+.
Then, we choose the new pairβ∗ which incurs the minimal cost ratio; i.e.,(24)β∗=Nisc′,MCSi′,Nirep′=argmin⁡Ciα,β∣β∈Ai-αand replace the default parameters by Nisc∗=Nisc′, MCSi∗=MCSi′, and Nirep∗=Nirep′ accordingly. Finally, go back to Step 2 for further allocation.Through the above steps, we can determine eachUEi’s subcarrier set Sisc, start time Tisc, and the corresponding configurations of MCSi, Nirep, and Pi while ensuring the delay deadline and reducing the waste of spectrum resource and energy.Below, we give an example in Figure4, where there are four scheduled UEs (UE1~UE4) and one UE (UE5) to be scheduled. The subframe indexes of DCIs for the four scheduled UEs are T1DCI=10, T2DCI=11, T3DCI=12, and T4DCI=13 (ms), separately. The current earliest subframe index for DCI is subframe 14 and scheduling subframe is Ts=14 (ms). Now, we consider schedule UE5, whose RU type is 3-tone, number of RUs is N5RU=1, total length is N5RU×(N5slot/2)=1×(8/2)=4 (ms), arrival time is T5req=4 (ms), and delay constraint is d5=20 (ms). From the current scheduling results, as shown in Figure 4(a), the available start time for each subcarrier is S0=19, S1=19, S2=19, S3=15, S4=15, S5=15, S6=16, S7=16, S8=16, S9=14, S10=14, and S11=21, respectively. Thus, the available subcarrier set for UE5 is S5sc∈{{0,1,2},{3,4,5},{6,7,8},{9,10,11}}. So, for the 4 possible subcarrier sets, the potential resource waste for UE5 is Waste(5,{0,1,2})=∑k′=3~11(max⁡{19,19,19}+1×(8/2)×1)+-S^k′=63, Waste(5,{3,4,5})=∑k′=0~2,6~11(max⁡{15,15,15}+1×(8/2)×1)+-S^k′=17, Waste(5,{6,7,8})=∑k′=0~5,9~11(max⁡{16,16,16}+1×(8/2)×1)+-S^k′=28, and Waste(5,{9,10,11})=∑k′=0~8(max⁡{15,15,21}+1×(8/2)×1)+-S^k′=87, which are the doted regions in Figures 4(b), 4(c), 4(d), and 4(e), respectively. Moreover, the subcarrier set of {9,10,11} in Figure 4(e) is infeasible because it violates the delay deadline of UE5 (i.e., maxk∈{9,10,11}S^k+(N5RU×(N5slot/2)×N5rep)=21+1×(8/2)×1=25≥(T5req+d5)=4+20=24). Thus, based on (21), the scheme chooses the best feasible subcarrier set S5sc∗={3,4,5} and the start time of UE5’s schedules RUs is T5sc=maxk∈{3,4,5}{S^k}=15 because it has the minimal value of Waste(5,{3,4,5})=17.Figure 4
Examples to scheduleUE5 based on the potential resource waste.
(a)
The scheduling results before schedulingUE5 (b)
The scheduling results if subcarrier set is{0,1,2} (c)
The scheduling results if subcarrier set is{3,4,5} (d)
The scheduling results if subcarrier set is{6,7,8} (e)
The scheduling results if subcarrier set is{9,10,11}


## 5. 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 N=3000~30000 UEs. Based on the model ofMAR (Mobile Autonomous Reporting) [8], the uplink requests of UEs arrive randomly with the data size of Di=50~200 bytes according to the Pareto distribution with α = 2.5. In addition, the interarrival time of requests includes 30 minutes (5%), 1 hour (15%), 2 hours (40%), and 1 day (40%), respectively.Table 5
The simulation parameters [7, 8].
Parameter Value maximum transmit power (Pimax) 23 dBm antenna gain of transmitter (Gi) −4 dBi antenna gain of receiver (GeNB) 18 dBi thermal noise density (N0) −174 dBm/Hz path loss (L(i,eNB)) 120.9 + 30.76log⁡(d) dB, d in Km distance from the base station 0~15 (Km) number of UEs (N) 3000~30000 request data size (Di) 50~200 bytes delay constraint (di) 50, 100, 150, 300 (ms) required reliability (Ri) 90 % ~ 99 %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 W1=0.5 and W2=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.


### 5.1. System Throughput

First, we investigate the effects of number of request UEs on system throughput. As shown in Figure5(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.Figure 5
Comparisons on the system throughput of all schemes.
(a) (b) (c) (d)We also investigate the effects of distribution of request data size on system throughput. As shown in Figure5(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, Figure5(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 Figure5(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.


### 5.2. Number of Serving UEs

Then, we investigate the effects of number of request UEs on number of serving UEs. As shown in Figure6(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.Figure 6
Comparisons on the number of serving UEs of all schemes.
(a) (b) (c) (d)We also investigate the effects of distribution of request data size on number of serving UEs. As shown in Figure6(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 Figure6(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 Figure6(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.


### 5.3. Packet Drop Rate

Then, we investigate the effects of number of request UEs on packet drop rate. As shown in Figure7(a), we can see that when the number of request UEs increases, the packet drop rate of all schemes increases due to network saturated gradually. Spec, Random, and RR perform 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.Figure 7
Comparisons on the packet drop rate of all schemes.
(a) (b) (c) (d)We also investigate the effects of distribution of request data size on packet drop rate. As shown in Figure7(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 Figure7(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 Figure7(d). As 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%.


### 5.4. Resource Consumption

Here, we investigate the effects of number of request UEs on resource consumption. As shown in Figure8(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.Figure 8
Comparisons on the resource consumption of all schemes.
(a) (b) (c) (d)Here, we also investigate the effects of distribution of request data size on resource consumption. As shown in Figure8(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 Figure8(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 Figure8(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.


### 5.5. Energy Consumption per UE

Finally, we investigate the effects of the number of request UEs on energy consumption per UE. As shown in Figure9(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 leverage the cost ratio to reduce energy consumption in phase 2, thus saving energy more efficiently.Figure 9
Comparisons on energy consumption per UE of all schemes.
(a) (b) (c) (d)In Figure9(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 Figure9(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. Figure9(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.


## 5.1. System Throughput

First, we investigate the effects of number of request UEs on system throughput. As shown in Figure5(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.Figure 5
Comparisons on the system throughput of all schemes.
(a) (b) (c) (d)We also investigate the effects of distribution of request data size on system throughput. As shown in Figure5(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, Figure5(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 Figure5(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.


## 5.2. Number of Serving UEs

Then, we investigate the effects of number of request UEs on number of serving UEs. As shown in Figure6(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.Figure 6
Comparisons on the number of serving UEs of all schemes.
(a) (b) (c) (d)We also investigate the effects of distribution of request data size on number of serving UEs. As shown in Figure6(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 Figure6(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 Figure6(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.


## 5.3. Packet Drop Rate

Then, we investigate the effects of number of request UEs on packet drop rate. As shown in Figure7(a), we can see that when the number of request UEs increases, the packet drop rate of all schemes increases due to network saturated gradually. Spec, Random, and RR perform 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.Figure 7
Comparisons on the packet drop rate of all schemes.
(a) (b) (c) (d)We also investigate the effects of distribution of request data size on packet drop rate. As shown in Figure7(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 Figure7(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 Figure7(d). As 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%.


## 5.4. Resource Consumption

Here, we investigate the effects of number of request UEs on resource consumption. As shown in Figure8(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.Figure 8
Comparisons on the resource consumption of all schemes.
(a) (b) (c) (d)Here, we also investigate the effects of distribution of request data size on resource consumption. As shown in Figure8(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 Figure8(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 Figure8(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.


## 5.5. Energy Consumption per UE

Finally, we investigate the effects of the number of request UEs on energy consumption per UE. As shown in Figure9(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 leverage the cost ratio to reduce energy consumption in phase 2, thus saving energy more efficiently.Figure 9
Comparisons on energy consumption per UE of all schemes.
(a) (b) (c) (d)In Figure9(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 Figure9(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. Figure9(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.


## 6. 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 energy-efficient and high-reliable scheme which has two phases. The first phase leverages the strategy of minimal energy cost to choose the default scheduling parameters with least energy consumption. The second phase exploits 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.



---

*Source: 4079017-2018-07-02.xml*