Joint time and power allocation for uplink cooperative non-orthogonal multiple access based massive machine-type communication Network

Abstract

Non-orthogonal multiple access is an essential promising solution to support large-scale connectivity required by massive machine-type communication scenario defined in the fifth generation (5G) mobile communication system. In this article, we study the problem of energy minimization in non-orthogonal multiple access–based massive machine-type communication network. Focusing on the massive machine-type communication scenario and assisted by grouping method, we propose an uplink cooperative non-orthogonal multiple access scheme with two phases, transmission phase and cooperation phase, for one uplink cooperative transmission period. Based on uplink cooperative non-orthogonal multiple access, the machine-type communication device with better channel condition and more residual energy will be selected as a group head, which acts as a relay assisting other machine-type communication devices to communicate. In the transmission phase, machine-type communication devices transmit data to the group head. Then, the group head transmits the received data with its own data to base station in the cooperation phase. Because the massive machine-type communication devices are low-cost dominant with limited battery, based on uplink cooperative non-orthogonal multiple access, we propose a joint time and power allocation algorithm to minimize the system energy consumption. Furthermore, the proposed joint time and power allocation algorithm includes dynamic group head selection and fractional transmit time allocation algorithms. Simulation results show that the proposed solution for uplink cooperative non-orthogonal multiple access–based massive machine-type communication network outperforms other schemes.

Keywords

Massive machine-type communication non-orthogonal multiple access uplink cooperative non-orthogonal multiple access joint time and power allocation energy minimization

Introduction

The deployment scenarios of the fifth generation (5G) system are grouped into three general categories: enhanced mobile broadband, ultra-reliable and low latency communications, and massive machine-type communications (mMTC). Among these three scenarios, machine-type communication (MTC) is known as machine to machine (M2M) communication, which is a form of data communication among several connected entities and does not necessarily need human interaction.¹ With the ever-increasing amount of connected devices and Internet of things (IoT) applications, the new services supported by MTC will sprout and promote the development of future 5G networks. However, there are challenges in enabling mMTC in 5G era.

Different from assumptions in current cellular networks for the conventional human-type communication (HTC) services, mMTC mainly focuses on uplink communications.² As machine-type communication devices (MTCDs) usually have small packets, low data rates, low cost and battery constrained, limited resources will become more precious when massive MTCDs access the network. Moreover, since current mobile networks are optimized to serve HTC, the optimizations may dissatisfy MTCDs’ requirement. There are several requirements and key performance indicators of mMTC should to be considered: coverage enhancements of 20 dB, 10 years device battery life, low device complexity and a few million devices per square kilometer.^3,4

To solve the aforementioned challenges, assisted by grouping, we propose an uplink cooperative non-orthogonal multiple access (UC-NOMA) scheme including transmission phase and cooperation phase for one uplink cooperative transmission period. Moreover, based on UC-NOMA, we propose a joint time and power allocation (JTPA) algorithm to minimize the system energy consumption, including dynamic group head selection and fractional transmit time allocation algorithms. The main contributions of this article are summarized as follows:

Exploiting the characteristic of NOMA technique that multiple MTCDs share the same subcarrier at the same time with different power levels, we propose an UC-NOMA scheme for mMTC networks. Furthermore, we characterize the total energy consumption of UC-NOMA–based mMTC networks, with transmission time and power allocation being taken into consideration.

The proposed UC-NOMA is based on a grouping method, where the distinctive channel gains of MTCDs are exploited. The MCTD with better channel condition and more residual energy will be selected as group head, which receives the data from member of MTCDs in the transmission phase and transmits the received data with its own data to base station (BS) in the cooperation phase.

Based on UC-NOMA, we propose the JTPA algorithm to minimize the energy consumption and prolong the lifetime of massive MTCDs. The dynamic group head selection and fractional transmission time allocation schemes are designed. The dynamic group head selection scheme enables the MTCDs with more residual energy and closer to BS to be the group head, and the fractional transmission time allocation scheme balances the transmission time allocated to each group.

The remainder of the article is organized as follows. The “Related works” section presents the review of the related works. The system model based uplink NOMA is described in section “System model.” The proposed dynamic group head selection and fractional transmission time allocation scheme are introduced in section “Joint Time and Power Allocation in UC-NOMA.” Section “Performance evaluations” provides the performance simulation results and section “Conclusion” concludes the article.

Related works

Instead of communicating with BS directly, MTCDs can associate with equipment functionally similar to relay and perform uplink multi-hop communication. Via uplink multi-hop communication in mMTC, not only intense competition against radio resources can be alleviated but also the energy consumptions of MTCDs with poor channel conditions can be reduced. The authors propose that the MTCDs first establish a link with machine-type communication gateway (MTCG), and then the MTCG communicates to BS with received data.⁵ Furthermore, considering that user equipment (UE) have more power and storage space than MTCDs, UE are configured as intermediate equipment.^6,7 But, the above schemes proposed are not appropriate for some scenarios without intermediate equipment.

The massive MTCDs’ accessing in 5G networks is one of the most challenges in mMTC networks. Some researchers focus on random access,⁸ while other researchers turn their attentions to NOMA instead of orthogonal multiple access (OMA). Although NOMA multiplexes multiple users in the same radio resource with increased co-channel interferences (CCIs), NOMA technology with employing power domain schedules more MTCDs to share the limited available resources.⁹ In addition, compared with conventional OMA, NOMA improves the overall system throughput and supports lower transmission latency and less signaling cost.¹⁰ These attractive characteristics drive NOMA to be a potential access technology for 5G system. And based on NOMA, massive connectivity per coverage with limited radio resources could be realized. Since massive MTCDs directly communicating with BS costs much overheads, grouping of MTCDs plays a key role in reducing the complexity. By modeling the system as a cooperative game in partition formation, two schemes are proposed to divide the users in a hybrid NOMA system.¹¹

In uplink NOMA system, the BS receives the multiplexed signals in power domain from different users and applies the successive interference cancelation (SIC) technology to decode each signal. The MTCD with highest channel gain is likely the strongest signal at the receiver and its signal will be decoded first. Then, the MTCD signal with the second highest channel gain is decoded and moving forward. Since NOMA systems depend on efficient SIC, the intra-group interference model needs to be adapted according to the level of SIC cancelations.¹² In particular, the use of SIC in NOMA facilitates MTCDs with better channel conditions to decode the messages of the other MTCDs, and furthermore, they also serve as relays to make the MTCDs with poor channel conditions access the cellular networks and reduce the energy consumption. To fully utilize the prior information about other users’ messages of the users with better channel conditions in downlink NOMA systems, a cooperative NOMA transmission scheme is proposed.¹³

Currently, most of researches focus on the downlink NOMA scenarios, while NOMA can serve general uplink and downlink scenarios with more than two users.¹⁴ The authors stand in different points to investigate the downlink NOMA, for example, fairness,^15,16 energy-efficient,^17,18 and sub-channel allocation.¹⁹ For uplink NOMA, an enhanced proportional fair (PF)-based scheduling scheme,²⁰ a suboptimal algorithm with single-user water-filling performed over all available sub-channels²¹ and a power back-off scheme based on fractional transmission power control²² are proposed.

MTCDs with limited battery have to serve for quite a long period, thus energy consumption becomes an urgent to be solved issue in mMTC networks. To save energy or extend service lifetime, each MTCD independently transmits its own signal with controlled transmission power. Power and energy efficiency about MTC are investigated in cellular networks and Long-Term Evolution (LTE) networks.^23,24 Based on traditional OMA schemes, the problem of minimizing the power consumption to prolong MTCDs’ lifetime is studied.²⁵ Furthermore, an uplink energy minimization problem to efficiently use the radio resources and support the mMTC is investigated for MTC with NOMA.⁷

System model

Consider an uplink NOMA system consisting of $M$ MTCDs randomly distributed in the sectors, as shown in Figure 1. All MTCDs are equipped with a single antenna. The sector is denoted by $S$ with radius $D_{S}$ . Denote the set of MTCDs as $M = {1, 2, \dots, M}$ . Without loss of generality, we assume that the MTCDs with poor channel conditions locate closely to the edge of the sector, while the MTCDs with better channel conditions locate around the center. To save the energy consumption of MTCDs with adverse locations, the MTCD with good channel condition plays a role of group head, which assists MTCDs with poor channel conditions to communicate. Therefore, this system is defined as UC-NOMA system.

Figure 1.

System model of an uplink cooperative NOMA single-cell network.

In NOMA, multiple MTCDs are multiplexed into transmission power domain and scheduled for transmission on the same spectrum resources non-orthogonally. In order to control the massive access and reduce the complexities of SIC, an MTCD grouping method is applied. The distinctness channel gains of different MTCDs is one of the key issues considered in minimizing CCI in a NOMA group. Moreover, to perform SIC at BS, we need to maintain the distinctness of the received signals. Thus, we divided the set of MTCDs $M$ into $K$ different groups by exploiting the distinctive channel gains. In the grouping method, first, the MTCDs are classified into Class 1 and Class 2 according to the channel gain. Second, according to the number of MTCDs $M$ and groups $K$ , the number of MTCDs in Class 1 is determined as $ϑ = max {K, M / 2}$ . The MTCDs in Class 1 have much lower channel gains compared to MTCDs in Class 2. Then, the channel gain is sorted as $h_{1} < h_{2} < \dots < h_{ϑ} < h_{ϑ + 1} < h_{ϑ + 2} < \dots < h_{M}$ , and $h_{m}$ is the channel gain from the $m^{th}$ MTCD to the destination. Furthermore, to keep the distinctive channel gain in one group, the MTCDs are also divided into different groups as follows: the channel gain of group-k set as ${h_{k}, h_{K + k}, h_{2 K + k}, \dots, h_{M - K + k}}$ .

The group-k set is denoted as $M_{k} = {1, 2, \dots, m_{k}} \cup {ℏ_{k}}$ , where $M_{k}$ represents the group member set and $ℏ_{k}$ represents the selected group head, $M_{k} \subseteq M, ℏ_{k} \in M$ . Furthermore, $\sum_{k = 1}^{K} (m_{k} + 1) = M$ .

In one UC-NOMA transmission period, there are two phases in time domain, transmission phase and cooperation phase, as shown in Figure 2. In the transmission phase, the transmission time allocated to group-k is denoted as $t_{k}$ , during which MTCDs in group-k transmit their data to their group head $ℏ_{k}$ , while the group head $ℏ_{k}$ keeps silent and receives the data. Constrained by the energy of MTCDs, assume that the received data are decoded by SIC at group head with help of multi-access edge computing (MEC),²⁶ which is running in the edge of network. MEC server can obtain network data, such as BS ID, available bandwidth, and information of the MTCDs’ location, which is used in SIC. Because we focus on the uplink communication of MTCDs and the total energy consumption of all MTCDs, the downlink phase of MEC information sent to the group heads and the processing time of MEC server are out scope of this article and not illustrated in Figure 2. In the cooperation phase, the last transmission time $t_{K + 1}$ is assigned to each group head $ℏ_{k}, k = 1, 2, \dots, K$ , which acts as relay and forwards the received data in the transmission phase with its own data to the BS. The transmission time of both two phases is constrained by $T$

\sum_{k = 1}^{K + 1} t_{k} \leq T

(1)

During the transmission phase of UC-NOMA for the group-k, MTCDs in group-k transmit their payloads to group head $ℏ_{k}$ , such as $r_{k, i}$ is the payload of $i th$ MTCD in group-k. The received signals in group head $ℏ_{k}$ are as follows

y_{ℏ_{k}} = \sum_{i = 1}^{m_{k}} \sqrt{p_{k, i}} s_{k, i} h_{k, i} + n_{k, i}

(2)

where $p_{k, i}$ , $s_{k, i}$ , $h_{k, i}$ , and $n_{k, i}$ are the parameters of $i th$ MTCD in group-k. $p_{k, i}$ denotes the transmission power, $s_{k, i}$ is the transmission signal with $| s_{k, i} |^{2} = 1$ , $h_{k, i}$ is the channel gain from itself to its group head $ℏ_{k}$ , and $n_{k, i}$ represents the additive Gaussian noise with $(0, σ^{2})$ .

Figure 2.

One uplink cooperative NOMA transmission period.

Joint Time and Power Allocation in UC-NOMA

Problem formulation

In uplink NOMA, the receiver exploits the SIC technology to decode the multiplexed signals in power domain. The channel gains of MTCDs in group-k are sorted as $H_{k} = {h_{k, 1} < h_{k, 2} \dots < h_{k, m_{k}}}$ . During the transmission time $t_{k}$ in UC-NOMA, each MTCD in group-k transmits data to group head $ℏ_{k}$ sharing the same bandwidth. Because the effect of the error propagation on NOMA performances caused by imperfect SIC is another challenge, in this article, we assume that perfect SIC is performed at receivers to obtain the upper bound of available data rate.²⁷ Under the condition of perfect SIC assumption, the MTCD with highest channel gain experiences interference from all other MTCDs, while the MTCD with lowest channel gain effectively enjoys interference-free transmission;⁸ thus, the achievable throughput of the $i th$ MTCD in group-k is given as follows⁷

R_{k, i} = B t_{k} \log (1 + \frac{p_{k, i} {| h_{k, i} |}^{2}}{\sum_{j = 1}^{i - 1} p_{k, j} {| h_{k, j} |}^{2} + σ^{2}})

(3)

where $B$ is the bandwidth of the uplink NOMA system for the whole group-k.

In the cooperation phase of UC-NOMA, during transmission time $t_{K + 1}$ , the group head $ℏ_{k}$ transmits the received data and its own $r_{ℏ_{k}}$ bits payload to the BS with power $q_{k}$ based on NOMA. The channel gain from group head $ℏ_{k}$ to BS is denoted as $g_{k}$ and the channel gains of group heads are sorted as $G = {g_{1} < g_{2} < \dots < g_{K}}$ . Thus, the achievable throughput of group head $ℏ_{k}$ is given as follows

R_{ℏ_{k}} = B t_{K + 1} \log (1 + \frac{q_{k} {| g_{k} |}^{2}}{\sum_{j = 1}^{k - 1} q_{j} {| g_{j} |}^{2} + σ^{2}})

(4)

Unlike traditional maximization of spectral efficiency for HTC, due to the features of mMTC, new principles are added to cellular networks. Consider that the battery lifetime is important for massive MTCDs and the uplink data transmission consumes a large portion of energy, we minimize energy consumption with a given payload

\begin{matrix} \min_{p, q, t} \sum_{k = 1}^{K} t_{k} \sum_{i = 1, i \in M_{k}}^{m_{k}} p_{k, i} + t_{K + 1} \sum_{k = 1}^{K} q_{k} \\ \begin{matrix} s . t . \sum_{k = 1}^{K + 1} t_{k} \leq T & (Co . 1) \\ 0 \leq p_{k, i} \leq p_{max, 1} & (Co . 2) \\ 0 \leq q_{k} \leq q_{max, 2} & (Co . 3) \\ R_{k, i} \geq r_{k, i}, i \in M_{k} & (Co . 4) \\ R_{ℏ_{k}} \geq r_{ℏ_{k}} + \sum_{i = 1, i \in M_{k}}^{m_{k}} R_{k, i} = {\bar{r}}_{ℏ_{k}} & (Co . 5) \end{matrix} \end{matrix}

(5)

where $p$ represents the transmission power of MTCDs in the transmission phase, $q$ denotes the transmission power of group heads in the cooperation phase, and $t$ is the transmission time. $r_{k, i}$ is the payload of MTCD $i$ in the group-k within time constraint $t_{k}$ and $r_{ℏ_{k}}$ is the payload of group head $ℏ_{k}$ itself within time constraint $t_{K + 1}$ . The total transmission time in the whole UC-NOMA should be less than $T$ as in (Co.1). Both (Co. 2) and (Co.3) require that neither MTCDs’ nor group heads’ transmission power is larger than their maximum transmission power. To guarantee the data transmission successfully, the throughput of MTCDs and MTCGs should meet the requirements in both (Co.4) and (Co.5).

In mMTC scenario, a large number of MTCDs with delay-tolerant transmit-limited size packet in low achievable rate extending the transmission time as long as possible will have benefits to the energy saving.⁶ In order to take full use of time and save energy, the total transmission time should be equal to $T$

\sum_{k = 1}^{K + 1} t_{k} = T

(6)

Furthermore, to save energy consumption, the (Co.5) and (Co.6) in equation (5) degenerate into

R_{k, i} = r_{k, i}, i \in M_{k}, R_{ℏ_{k}} = r_{ℏ_{k}} + \sum_{i = 1, i \in M_{k}}^{m_{k}} R_{k, i} = {\bar{r}}_{ℏ_{k}}

(7)

According to equations (3), (4), and (7), we obtain

p_{k, i} {| h_{k, i} |}^{2} = (2^{\frac{r_{k, i}}{B t_{k}}} - 1) (\sum_{j = 1}^{i - 1} p_{k, j} {| h_{k, j} |}^{2} + σ^{2})

(8)

With the help of recursion method

p_{k, 1} {| h_{k, 1} |}^{2} = (2^{\frac{r_{k, 1}}{B t_{k}}} - 1) σ^{2}

(9a)

\begin{matrix} p_{k, 2} {| h_{k, 2} |}^{2} = (2^{\frac{r_{k, 2}}{B t_{k}}} - 1) (p_{k, 1} {| h_{k, 1} |}^{2} + σ^{2}) \\ = (2^{\frac{r_{k, 2}}{B t_{k}}} - 1) (2^{\frac{r 1}{B t_{k}}}) σ^{2} \end{matrix}

(9b)

p_{k, i} {| h_{k, i} |}^{2} = (2^{\frac{r_{k, i}}{W t_{k}}} - 1) (2^{\frac{r_{k, i - 1}}{W t_{k}}}) \dots (2^{\frac{r_{k, 1}}{W t_{k}}}) σ^{2}

(9c)

we have

p_{k, i} = {\begin{matrix} \frac{σ^{2}}{{| h_{k, i} |}^{2}} (2^{\frac{r_{k, i}}{B t_{k}}} - 1) & i = 1 \\ \frac{σ^{2}}{{| h_{k, i} |}^{2}} (2^{\frac{r_{k, i}}{B t_{k}}} - 1) 2^{\frac{{\hat{r}}_{k, i}}{B t_{k}}} & i > 1 \end{matrix}

(10a)

q_{k} = {\begin{matrix} \frac{σ^{2}}{{| g_{k} |}^{2}} (2^{\frac{{\bar{r}}_{ℏ_{k}}}{B t_{K + 1}}} - 1) & k = 1 \\ \frac{σ^{2}}{{| g_{k} |}^{2}} (2^{\frac{{\bar{r}}_{ℏ_{k}}}{B t_{K + 1}}} - 1) 2^{\frac{{\hat{r}}_{ℏ_{k}}}{B t_{K + 1}}} & k > 1 \end{matrix}

(10b)

where ${\hat{r}}_{k, i} = \sum_{j = 1}^{i - 1} r_{k, j}$ and ${\hat{r}}_{ℏ_{k}} = \sum_{l = 1}^{k - 1} {\bar{r}}_{ℏ_{l}}$ .

Thus, the original problem (5) can be converted as minimizing the energy consumption subjected to transmission time

\begin{matrix} \min_{p, q, t} \sum_{k = 1}^{K} t_{k} \sum_{i = 1, i \in M_{k}}^{m_{k}} \frac{σ^{2}}{{| h_{k, i} |}^{2}} (2^{\frac{r_{k, i}}{B t_{k}}} - 1) 2^{\frac{{\hat{r}}_{k, i}}{B t_{k}}} \\ + t_{K + 1} \sum_{k = 1}^{K} \frac{σ^{2}}{{| g_{k} |}^{2}} (2^{\frac{{\bar{r}}_{ℏ_{k}}}{B t_{K + 1}}} - 1) 2^{\frac{{\hat{r}}_{ℏ_{k}}}{B t_{K + 1}}} \\ s . t . \begin{matrix} \sum_{k = 1}^{K + 1} t_{k} = T & (Co . 1) \\ τ_{k} \leq t_{k} \leq t_{K + 1} & (Co . 2) \end{matrix} \end{matrix}

(11)

Problem (11) is proved to be a convex function in Appendix 1. And, we can employ Lagrangian function to minimize the energy consumption in equation (11).²⁸

Resource allocation algorithm

In equation (10), the transmission power is a monotonically decreasing function with transmission time. Although the original problem is proved to be convex and the globally optimal solution can be obtained via interior point method, the complexity is high. To save energy, we trade off the transmission time between the transmission phase and the cooperation phase in the UC-NOMA. Assuming that the transmission time of cooperation phase is $t_{K + 1} = β T$ , $β$ is the time factor and $β \in (0, 1)$ and the total transmission time of transmission phase is $T_{1} = (1 - β) T$ . Problem (11) is converted into

\begin{matrix} min_{p, q, t} \sum_{k = 1}^{K} t_{k} \sum_{i = 1, i \in M_{k}}^{m_{k}} \frac{σ^{2}}{{| h_{k, i} |}^{2}} (2^{\frac{r_{k, i}}{B t_{k}}} - 1) 2^{\frac{{\hat{r}}_{k, i}}{B t_{k}}} \\ s . t . \sum_{k = 1}^{K} t_{k} = T_{1} \end{matrix}

(12)

In practical conditions, MTCDs with limited computing ability and battery constrained have to process some complex operations without other equipment assisted. The more residual energy remains, the longer lifetime MTCD has. Therefore, based on the residual energy and geographic information of MTCD, we dynamically selected the group head to extend its lifetime in different transmission periods. To reduce the energy consumption and guarantee the information upload from the remote location MTCDs, the MTCD close to the BS is easy to be chosen as group head. The normalized function consisted of distance and residual energy is

W_{k, i} (n) = \sqrt{{(α_{1} {\bar{d}}_{k, i})}^{2} + {(α_{2} {\bar{Q}}_{k, i} (n))}^{2}}

(13)

where $W_{k, i} (n)$ is the corresponding normalized function of the $i th$ MTCD in group-k during the $n th$ period, $α_{1}$ and $α_{2}$ are the weights factor of normalized distance ${\bar{d}}_{k, i} = d_{max} / d_{k, i}$ and normalized residual energy ${\bar{Q}}_{k, i} (n) = Q_{k, i} (n) / Q_{max}$ . $Q_{k, i} (n)$ is the residual energy of the $i th$ MTCD in group-k at the beginning of the $n th$ period

Q_{k, i} (n) = Q_{k, i} (n - 1) - p_{k, i}^{*} (n - 1) t_{k, i}^{*} (n - 1)

(14)

where $p_{k, i}^{*} (n - 1)$ and $t_{k, i}^{*} (n - 1)$ are the optimal transmission power and time of the $i th$ MTCD in group-k during the $n th$ period.

As shown in equation (3), the transmission time is inversely proportional to channel gain with given transmission power of MTCDs in group-k. In addition, the transmission time also has an impact on the residual energy, which determines the lifetime of one group. Thus, with taking channel gain and residual energy into consideration, we proposed fractional transmit time allocation strategy to balance the energy consumption of the MTCDs group

t_{k} (n) = \frac{{[Min {Q_{k, i} (n) {\bar{h}}_{l, i}}_{1}^{l}]}^{- δ}}{\sum_{k = 1}^{K} {[Min {Q_{k, i} (n) {\bar{h}}_{l, i}}_{1}^{l}]}^{- δ}} T_{1}

(15)

where $t_{k} (n)$ is the transmission time allocated to MTCDs in group-k during the $n th$ period, ${\bar{h}}_{k, i} = | | h_{k, i} | | / | | h_{max} | |$ is the normalized channel gain, and $δ (0 \leq δ \leq 1)$ is a decay factor. In the case of $δ = 0$ , it corresponds to equal time allocation among the $K$ groups. In equation (15), it is clear that when $δ$ increases, more time is allocated to the MTCD with less residual energy and poor channel gain. The JTPA algorithm consists of dynamic group head selecting, and fractional transmit time allocation is described in Algorithm 1. The total computational complexities of power allocation for three schemes are same, which is $O (M)$ . The total computational complexities of time allocation for $O (K + 1)$ , $O (K + 1)$ , and $O (2 K + 2)$ for JTPA-NOMA, PBO-NOMA, OPA-TDMA, respectively.

Algorithm 1: Joint Time and Power Allocation algorithm
1 Feedback Energy Information: All the MTCDs in one group send their energy information $Q_{k, i} (n)$ to the central controller. 2 Dynamic Group Head Selecting: At the beginning of the $n th$ period, according to equation (14) the central controller determine the group head of each group and the required transmission time $t_{K + 1}$ in the cooperation stage UC-NOMA, the group head determine their transmission power based on equation (10). 3 Fractional Transmit Time Allocation: The central controller according to equation (15) derive the parameters ${t_{k} (n)}$ and feed back to the MTCDs of each group. 4 Power allocation: After receiving the above parameters, each MTCD determines the optimal transmission power with equation (10). 5 Residual-energy Updating: At the end of the $n th$ period, each of the MTCDs should update its residual-energy through equation (14).

Algorithm 1: Joint Time and Power Allocation algorithm

1 Feedback Energy Information: All the MTCDs in one group send their energy information

Q_{k, i} (n)

to the central controller.
2 Dynamic Group Head Selecting: At the beginning of the

n th

period, according to equation (14) the central controller determine the group head of each group and the required transmission time

t_{K + 1}

in the cooperation stage UC-NOMA, the group head determine their transmission power based on equation (10).
3 Fractional Transmit Time Allocation: The central controller according to equation (15) derive the parameters

{t_{k} (n)}

and feed back to the MTCDs of each group.
4 Power allocation: After receiving the above parameters, each MTCD determines the optimal transmission power with equation (10).
5 Residual-energy Updating: At the end of the

n th

period, each of the MTCDs should update its residual-energy through equation (14).

Performance evaluations

In this section, we provide simulations to evaluate the performance of JTPA in the proposed UC-NOMA–based mMTC scenario. The details of simulation parameters are given in Table 1. We refer to the proposed algorithm as JTPA-NOMA and take two other schemes, optimal power allocation based on TDMA (OPA-TDMA)⁶ and the power back-off scheme in uplink NOMA (PBO-NOMA),²² for comparison. The transmission power of MTCD will exceed the maximum transmission power limit, under heavy payload, poor channel condition, and severe CCI. The JTPA-NOMA, PBO-NOMA, and OPA-TDMA schemes will block the MTCD that exceeds the maximum transmission power. If an MTCD is blocked, the energy consumption of the MTCD is set to 0.

Table 1.

Simulation parameters.

Parameter	Value range
Inter-site distance	500 m
Transmission bandwidth	180 kHz
Payload of each MTCD⁶	1 kbit
Maximum transmission power^6,7	14 dBm
Noise	−174 dBm/Hz
Total energy of each MTCD⁷	1 J
Transmission time T⁶	1 s
Distance-dependent path loss²⁹	Based on 3GPP 36.843

MTCD: machine-type communication device.

Besides PBO-NOMA, both JTPA-NOMA and OPA-TDMA minimize the energy consumption and prolong the network lifetime; thus, we set PBO-NOMA as a baseline to illustrate the relationship between network lifetime and the number of MTCDs. With the same total energy of each MTCD, the network lifetime is evaluated by the period the first MTCD runs out of its energy. The Y-axis of Figure 3 depicts the normalized network lifetime, which is defined as the ratio of network lifetime of JTPA-NOMA and OPA-TDMA to network lifetime of baseline PBO-NOMA. The number of group is set as 50 and the time factor of cooperation phase in UC-NOMA is set as 0.05 to simulate a worse case.

Figure 3.

The normalization network lifetime of baseline versus the number of MTCDs.

In Figure 3, it can be clearly seen that the lifetime of JTPA-NOMA is few or hundred times to that of PBO-NOMA. With the number of MTCDs increasing, the MTCDs in each group will increase. MTCDs have to increase transmission power to successfully upload their payloads under server CCI; this directly leads to the increase in energy consumption and decrease in mMTC networks’ lifetime.

Figure 4 shows the average energy consumption and the average power consumption for different MTCDs within total time $T$ . The average energy consumption and average power consumption are defined as the average energy and power consumed by each MTCD in the transmission time $T$ . The curve is obtained by varying the number of MTCD from 30 to 300. The performance of average energy and average power for JTPA-NOMA is superior to PBO-NOMA and OPA-TDMA. For the schemes of NOMA, that is, JTPA-NOMA and PBO-NOMA, due to the number of MTCDs in each group increases with the total number of MTCDs, MTCDs have to pay more transmission power to overcome CCI and successfully communicate with group head, which leads the average energy and average power increase with MTCDs’ number. Because too many MTCDs divided into a group will be blocked when the members of each group reach to a certain value, the energy consumption and power consumption will keep in a certain value.

Figure 4.

Average energy and power versus different MTCD numbers.

Figure 5 shows the average energy consumption and the average power consumption of all MTCDs in the UC-NOMA within total time $T$ . The curve is obtained by varying the time factor of cooperation phase in UC-NOMA from 0.05 to 0.95. It is obvious that the time factor of cooperation phase has great influence on JTPA-NOMA and PBO-NOMA; besides, JTPA-NOMA outperforms PBO-NOMA and TDMA. With the increase in transmission time of cooperation phase, the average energy consumption of JTPA-NOMA declines. This is because transmission time is an important factor affecting energy consumption. The increase in the transmission time in cooperation phase causes the group head to communicate with BS with a lower power. While with the decrease in transmission time of transmission phase, the group member in the transmission phase has to increase its transmission power to communication, and more MTCDs will fail to communicate since the transmission power exceeds the maximum transmission power.

Figure 5.

Average energy and power versus different time factors.

Figure 6 shows the average energy consumption and average power consumption versus different number of groups within total time $T$ . The curve is obtained by varying the number group from 35 to 70. We can find that the average energy and power performance of JTPA-NOMA outperform those of PBO-NOMA and OPA-NOMA. With the increase in the number of groups, fewer MTCDs are divided into a group and less CCI is generated, and the MTCDs deliver data with a lower transmission power. Thus, the average energy and average power of JTPA-NOMA decrease with the increase in the number of groups.

Figure 6.

Average energy and power versus different group numbers.

Finally, in Figure 7, we illustrate the average energy efficiency versus different number of groups within total time $T$ . The curve is obtained by varying the group number from 35 to 70. Standing in a point of energy efficiency, the JTPA-NOMA outperforms than PBO-NOMA and OPA-NOMA. As the number of groups increases, more MTCDs successfully transmit with less transmission power with fewer MTCDs divided into a group and less CCI generated; thus, the energy efficiency increases. Furthermore, with the same number of groups, the larger number of MTCDs will consume more energy and powers and have higher energy efficiency, which is shown in Figures 6 and 7. This is because the members of one group increase with the number of MTCDs, and MTCDs have to consume more transmission powers to overcome the increased CCI and successfully communicate.

Figure 7.

Average energy efficiency versus different group numbers.

Conclusion

In this article, the time allocation and power control problems in UC-NOMA–based mMTC network were jointly studied, with the aim of minimizing the energy consumption and prolonging the network lifetime. By exploiting the distinctive channel gains of MTCDs, an MTCD grouping method is introduced to control the massive MTCDs’ access. Furthermore, a UC-NOMA scheme is proposed, where the MTCD with poor channel condition transmits its data to the group head in the transmission phase; then, the group head transmits its own data and received data to the BS in the cooperation phase. Based on the proposed dynamic group head selection scheme, the MTCD with more residual energy and closer to BS is selected to be the group head. In addition, fractional transmission time allocation scheme is proposed to solve the problem of JTPA. Simulation results have shown that the proposed JTPA outperforms the PBO-NOMA and OPA-TDMA in terms of energy minimization.

Footnotes

Appendix 1

This part aims to prove problem (9) ia a convex function. Problem (9) can be written as follows

(16)

\begin{matrix} \sum_{k = 1}^{K} t_{k} \sum_{i = 1, i \in M_{k}}^{m_{k}} p_{k, i} + t_{K + 1} \sum_{k = 1}^{K} q_{k} \\ = \sum_{k = 1}^{K} t_{k} \sum_{i = 1, i \in M_{k}}^{m_{k}} \frac{σ^{2}}{{| h_{k, i} |}^{2}} (2^{\frac{r_{k, i}}{B t_{k}}} - 1) 2^{\frac{{\hat{r}}_{k, i}}{B t_{k}}} \\ + t_{K + 1} \sum_{k = 1}^{K} \frac{σ^{2}}{{| g_{k} |}^{2}} (2^{\frac{{\bar{r}}_{ℏ_{k}}}{B t_{K + 1}}} - 1) 2^{\frac{{\hat{r}}_{ℏ_{k}}}{B t_{K + 1}}} \end{matrix}

Assuming that $X_{k, i} = r_{k, i} / W t_{k}, {\hat{X}}_{k, i} = {\hat{r}}_{k, i} / W t_{k}, Y_{k} = {\bar{r}}_{ℏ_{k}} / W t_{K + 1}, {\hat{Y}}_{k} = {\hat{r}}_{ℏ_{k}} / W t_{K + 1}$ , of which the first derivation is

(17)

\begin{matrix} \frac{\partial X_{k, i}}{\partial t_{k}} = - \frac{X_{k, i}}{t_{k}}, \frac{\partial {\hat{X}}_{k, i}}{\partial t_{k}} = - \frac{{\hat{X}}_{k, i}}{t_{k}} \\ \frac{\partial Y_{k}}{\partial t_{K + 1}} = - \frac{Y_{k}}{t_{K + 1}}, \frac{\partial {\hat{Y}}_{k}}{\partial t_{K + 1}} = - \frac{{\hat{Y}}_{k}}{t_{K + 1}} \end{matrix}

Equation (16) is rewritten as follows

(18)

\begin{matrix} \sum_{k = 1}^{K} t_{k} \sum_{i = 1, i \in M_{k}}^{m_{k}} p_{k, i} + t_{K + 1} \sum_{k = 1}^{K} q_{k} \\ = \sum_{k = 1}^{K} t_{k} \sum_{i = 1, i \in M_{k}}^{m_{k}} \frac{σ^{2}}{{| h_{k, i} |}^{2}} (2^{X_{k, i}} - 1) 2^{{\hat{X}}_{k, i}} \\ + t_{K + 1} \sum_{k = 1}^{K} \frac{σ^{2}}{{| g_{k} |}^{2}} (2^{Y_{k}} - 1) 2^{{\hat{Y}}_{k}} \\ = \sum_{k = 1}^{K} E_{k} + E_{K + 1} \end{matrix}

where

(19)

\begin{matrix} E_{k} = t_{k} \sum_{i = 1, i \in M_{k}}^{m_{k}} \frac{σ^{2}}{{| h_{k, i} |}^{2}} (2^{X_{k, i}} - 1) 2^{{\hat{X}}_{k, i}} \\ E_{K + 1} = t_{K + 1} \sum_{k = 1}^{K} \frac{σ^{2}}{{| g_{k} |}^{2}} (2^{Y_{k}} - 1) 2^{{\hat{Y}}_{k}} \end{matrix}

With the first derivation of $E_{k}$ , we have

(20)

\begin{matrix} \frac{\partial E_{k}}{\partial t_{k}} = & \sum_{i = 1, i \in M_{k}}^{m_{k}} \frac{σ^{2}}{{| h_{k, i} |}^{2}} (2^{X_{k, i}} - 1) 2^{{\hat{X}}_{k, i}} \\ + t_{k} \sum_{i = 1, i \in M_{k}}^{m_{k}} \frac{σ^{2}}{{| h_{k, i} |}^{2}} (2^{X_{k, i}} \ln 2 (- \frac{X_{k, i}}{t_{k}}) 2^{{\hat{X}}_{k, i}}) \\ + t_{k} \sum_{i = 1, i \in M_{k}}^{m_{k}} \frac{σ^{2}}{{| h_{k, i} |}^{2}} (2^{X_{k, i}} - 1) 2^{{\hat{X}}_{k, i}} \ln 2 (- \frac{{\hat{X}}_{k, i}}{t_{k}}) \\ = \sum_{i = 1, i \in M_{k}}^{m_{k}} \frac{σ^{2} 2^{{\hat{X}}_{k, i}}}{{| h_{k, i} |}^{2}} [(2^{X_{k, i}} - 1) - 2^{X_{k, i}} \ln 2 (X_{k, i})] \\ - \sum_{i = 1, i \in M_{k}}^{m_{k}} \frac{σ^{2} 2^{{\hat{X}}_{k, i}}}{{| h_{k, i} |}^{2}} (2^{X_{k, i}} - 1) \ln 2 ({\hat{X}}_{k, i}) \end{matrix}

Furthermore, given that

(21)

\begin{matrix} A = 2^{{\hat{X}}_{k, i}}, B = 2^{X_{k, i}} - 1 \\ C = 2^{X_{k, i}} \ln 2 (X_{k, i}), D = (2^{X_{k, i}} - 1) \ln 2 ({\hat{X}}_{k, i}) \end{matrix}

we have

(22)

\begin{matrix} \frac{\partial A}{\partial t_{k}} = 2^{{\hat{X}}_{k, i}} \ln 2 (- \frac{{\hat{X}}_{k, i}}{t_{k}}) \\ \frac{\partial B}{\partial t_{k}} = 2^{X_{k, i}} \ln 2 (- \frac{X_{k, i}}{t_{k}}) \\ \frac{\partial C}{\partial t_{k}} = 2^{X_{k, i}} \ln 2 (- \frac{X_{k, i}}{t_{k}}) (\ln 2 (X_{k, i}) + 1) \\ \frac{\partial D}{\partial t_{i}} = 2^{X_{k, i}} \ln 2 (- \frac{X_{k, i}}{t_{k}}) \ln 2 ({\hat{X}}_{k, i}) \\ + (2^{X_{k, i}} - 1) \ln 2 (- \frac{{\hat{X}}_{k, i}}{t_{k}}) \end{matrix}

With the second derivation of $E_{k}$ , we have

(23)

\begin{matrix} \frac{\partial^{2} E_{k}}{\partial {(t_{k})}^{2}} = \sum_{i = 1, i \in M_{k}}^{m_{k}} \frac{σ^{2}}{{| h_{k, i} |}^{2}} [\frac{\partial A}{\partial t_{i}} (B - C - D)] \\ + \sum_{i = 1, i \in M_{k}}^{m_{k}} \frac{σ^{2}}{{| h_{k, i} |}^{2}} A [\frac{\partial B}{\partial t_{i}} - \frac{\partial C}{\partial t_{i}} - \frac{\partial D}{\partial t_{i}}] \\ = \sum_{i = 1, i \in M_{k}}^{m_{k}} \frac{σ^{2} 2^{{\hat{X}}_{k, i}} {(\ln 2)}^{2}}{{| h_{k, i} |}^{2} t_{k}} [2^{X_{k, i}} {({\hat{X}}_{k, i} + X_{k, i})}^{2}] \\ - \sum_{i = 1, i \in M_{k}}^{m_{k}} \frac{σ^{2} 2^{{\hat{X}}_{k, i}} {(\ln 2)}^{2}}{{| h_{k, i} |}^{2} t_{k}} {({\hat{X}}_{k, i})}^{2} \\ \geq 0 \end{matrix}

The same can be obtained

(24)

\frac{\partial^{2} E_{K + 1}}{\partial {(t_{K + 1})}^{2}} \geq 0

Thus, Problem (9) is convex function of transmission time.

Handling Editor: Wei Ni

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This paper is supported by National Key R&D Program of China no. 2017YFB0801702, Beijing Natural Science Foundation no. L172033, National Natural Science Foundation of China no. 61471068, and 111 Project of China B16006.

ORCID iD

Shujun Han

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