Device-to-device and mobile user communication with queuing in NOMA-based network

In 3G- and 4G-based networks, orthogonal multiple access (OMA) techniques were commonly used for resource allocation to users for improving spectral efficiency (Balyan and Saini, 2011, 2014; Balyan et al., 2018; Saini and Balyan, 2012). For 5G and beyond networks, non-orthogonal multiple access (NOMA) proves out better than the conventional orthogonal multiple access (OMA) techniques due to a large number of users with higher speed requirements. This is mainly due to the requirements of OMA to maintain orthogonality (Rabie and Adebisi, 2017). NOMA allows a single transmitter using the same frequency to send multiple signals for multiple users, the multiple signals use superposition of power, which improves overall spectrum efficiency (Balyan, 2020; Balyan and Daniels, 2020; Ding et al., 2017). Device-to-device (D2D) communication can be used to establish direct communication between users without getting processed through a base station (BS) or other backbone networks. This help reducing the transmission power of users and the traffic loads of BS (Ahmed et al., 2018; Liu et al., 2015). The D2D communication combined with NOMA got attention recently. The combination of both D2D communication and NOMA technology allows more users to be serviced at a time in the network. The BS transmits to multiple mobile users using NOMA (Pan et al., 2018). While keeping the minimum requirements condition of mobile users, the D2D users total rate is maximized. A channel allocation algorithm, which maximizes the total rate of the network, is proposed in Zhao et al. (2018), after analyzing D2D users’ rates using NOMA technology. The work in the study of Arachchillage et al. (2018) summarizes the recent advances and future research challenges of NOMA. The work also demonstrates how the inclusion of NOMA impacts D2D performance, radio frequency, energy harvesting, multiple input multiple output (MIMO), and other emerging 5G technologies. When D2D pairs and mobile users communicate in the presence of each other mutual interference exists, appropriate power control methods need to be implemented to ensure signal to interference plus noise ratio (SINR) is above a certain threshold level for guaranteed quality of service (QoS). Another factor that is influenced due to the presence of D2D pairs and mobile users simultaneously is a delay or the latency, which is an important factor for time-sensitive applications. If both physical layer and latency need to be improved together, the channel state and queuing at each device needs to be known before transmitting and receiving. For a user with a probability of higher latency due to the long queue and with a weak channel that can be used, power control and resource allocation should be in place to overcome the problem of latency and weak channel.

Some of the work in the literature addresses latency in D2D communication. The work in the study of Cui et al. (2012) uses the Large Deviation Theory, which uses equivalent rate constraints that are derived from equivalent latency constraints. The authors in the study of Cui et al. (2012) also use the Lyapunov Drift Theory for queue stabilization.

The work in the study of Cui et al. (2012) was used (Li et al., 2017) for the latency analysis of the D2D pairs, and is concluded that D2D pairs latency depends on the order of data arrival and type. Another approach named Stochastic majorization is used in Asheralieva and Miyanaga (2016) that implements the longest queue highest rate possible approach for providing a power control, which is latency aware. This perfectly works for the networks where data arrivals are consistent in type and rate. Markov Decision Process (MDP) is also used for optimal resource control for wireless systems with latency issues. Wang et al. (2015) derive an approximation of MDP for modeling the dynamic power control in D2D communication, which is latency aware. The complexity is reduced by assuming that the Medium Access Control (MAC) layer has interference filtering property.

The work in the study of Xu et al. (2020) is done to address the latency issues and to find out the trade-off between reliability and block length. The finite block length codes (FBCs) capacity approximation is adopted in place of the Shannon Capacity formula. To cope with the latency constraints and to explicitly specify the trade-off between block length (latency) and reliability, the normal approximation of the capacity of finite block length codes (FBCs) is adopted, in contrast to the classical Shannon capacity formula. NOMA is used as a transmission scheme. An interference alignment (IA) and independent component analysis (ICA) (IA–ICA)-based semi-blind scheme is proposed in Wan et al. (2020). The NOMA-based transmission provides a better symbol error rate (SER) than existing approaches in the literature with high reliability and low latency. The authors in Xin et al. (2019) develop a spatiotemporal mathematical model for analyzing the performance of the mobile network with prioritized data transmissions. For D2D users, a dynamic interference model is constructed using thinned Poisson point process to set D2D users location and buffer to store data. A priority queuing model is used for variable rate traffic arrival. The work in this paper is done to address the issue of latency when D2D pairs communicate in an underlying mobile network. NOMA-based communication is adopted for transmission hybridized with TDMA for bit and time allocation. It is less complex also.

The work in this paper is described as follows. The system model and proposed work are given in the second section. The problem is formulated in the third section. The simulation results are demonstrated and explained in the fourth section. Finally, the paper is concluded.

Proposed work

In the considered cellular network, a single cell environment is taken that consists of a base station (BS), mobile user (MU), and D2D pairs denoted by $1\le n_{D2D}\le N$. The D2D pairs use the uplink resources of MU. The mutual interference present between MUs and D2D pairs. The nomenclature and abbreviation are given in Table 1. The time is divided into F time slots of duration $t_s$ for the transmission of a frame. The total time required for transmission of a frame is $T_F=F{t}_s$. In one-time slot, the MU uplink transmission and one of the D2D pairs’ communication takes place. A non-orthogonal multiple access (NOMA) scheme is used for channel sharing between them. NOMA uses successive interference cancellation (SIC) to decode signals. For a two-user network denoted as 1 and 2, NOMA uses SIC based on their channel condition. If user 1 is close to BS, i.e. $|h_1{|}^2>|h_2{|}^2(h_1,h_2~CN(0,\lambda ))$. User 1 will decode signal of user 2 (strong power) first and then its signal. The signal to interference and noise ratio (SINR) of the decoded signals is:

Table 1.

Nomenclature and abbreviations.

After removing SINR decoded for user 2, the decoded SINR for user 1 signal is:

(2)

$$\begin{array}{}\text{(2)}& SIN{R}_f^1=\frac{a_1(f)P_s(f)|h_1{|}^2}{{\sigma }^2}.\end{array}$$

The decoded SINR for user 2 signal with interference from user 1 considered as noise is:

(3)

$$\begin{array}{}\text{(3)}& SIN{R}_f^2=\frac{a_2(f)P_s(f)|h_2{|}^2}{a_1(f)P_s(f)|h_2{|}^2+{\sigma }^2},\end{array}$$

(3)where $P_s$ denotes total power allocated to BS and $a_1,a_2$ denotes power allocation coefficients to user 1 and user 2, respectively, ${\sigma }^2$ is variance of Additive White Gaussian Noise (AWGN). Also, $a_1<a_2$ and $a_1+a_2=1$.

The achieved data rate and throughput for user 1 in time slot f is:

(4)

$$\begin{array}{}\text{(4)}& R_1(f)=f\times {\log }_2(1+SIN{R}_f^1)andT{H}_1(f)=n_{RB}(f)B{R}_1(f).\end{array}$$

The achieved data rate and throughput for user 2 in time slot f is:

(5a)

$$\begin{array}{}\text{(5a)}& R_2(f)=f\times {\log }_2(1+\min (SIN{R}_f^2,SIN{R}_f^{2-1})),\end{array}$$

(5a)

(5b)

$$\begin{array}{}\text{(5b)}& T{H}_2(f)=n_{RB}(f)B{R}_2(f).\end{array}$$

The data arrival at D2D transmitter is with a rate ${\lambda }_m$ bits per second. The data or call rate of the MU is ${\lambda }_u$ bits per second. Due to the existence of the actual interference when cellular network channels are shared by D2D users, in each time slot SINR value is used to determine the server process. A low priority and high priority is also set at each transmitter queue. The D2D transmitter has a buffer where it can queue data to be transmitted and has a threshold value of $Q_m^{max}$, $,1\le m\le M,m$ denotes the $m^{th}$ transmitter. For a queue length $Q_m(f),$, where $Q_m(f)<Q_m^{max}$ in $f^{th}$ time slot can be determined as:

(6)

$$\begin{array}{}\text{(6)}& Q_m(f)=\{\begin{array}{c}{Q}_m(f-1)+{\lambda }_m{t}_s\\ Q_m(f-1)+{\lambda }_m{t}_s-R\text{'}(f)/t_s\end{array}\}=Q_m(f-1)+{\lambda }_m{t}_s-b_m(f)R_m^{\text{'}}(f)/t_s,\end{array}$$

(6)where $b_m(f)$ is Boolean and have two values 1 and 0. 1: channel is used in $f^{th}$ time slot by $m^{th}$ D2D pair and 0: channel is not used:When $R_c\ge ({\lambda }_{d_m}{t}_s+\mathrm{overhead}\mathrm{bits})/t_s,$

(7)

$$\begin{array}{}\text{(7)}& R_m^{\text{'}}(f)={\lambda }_{d_m}{t}_s+\mathrm{overhead}\mathrm{bits}.\end{array}$$

(7) When $R_c<({\lambda }_{d_m}{t}_s+\mathrm{overhead}\mathrm{bits})/t_s$

(8)

$$\begin{array}{}\text{(8)}& R_m^{\text{'}}(f)/t_s=R_c,\end{array}$$

where $R_c$ denotes the data rate of channel, which is given by Shannon Theorem:

(9)

$$\begin{array}{}\text{(9)}& R_c=Blo{g}_s(1+SIN{R}_m)\end{array}$$

A $m^{th}$ D2D transmitter is allowed to transmit or not depends upon the received $SINR$ is above a certain threshold defined for the network or application, i.e. $SIN{R}_m\ge SIN{R}_m^{Th}$. When the buffer queue length $Q_m(f)=Q_m^{max}$, the packets arriving later are dropped. The model uses the first-in-first-out (FIFO) queue discipline for the transmission of the packets. When there is a requirement of service with priority, the packet is placed at the head of the queue or thereafter, if the head of the queue is also a priority packet. The queuing delay (latency) experienced by $m^{th}$ transmitter in $f^{th}$ can be derived from Little’s law:

(10)

$$\begin{array}{}\text{(10)}& t_{dm}=\frac{{\sum }_{m=1}^M{Q}_m}{{\lambda }_m{t}_s},\end{array}$$

(10)where $Q_m$ denotes the length of queue when $m^{th}$ transmitter is selected for transmission. Also, for maximum admissible latency, if the time is $t_{d_{max}}$ while in a particular time slot, $t_{dm}<t_{d_{max}}$.

Problem formulation

In uplink transmission of mobile users, the data sent by MU that is using a subchannel l with expectation $E\{|x_l{|}^2\}=1$, where $x_l$ denotes the data sent by MU. The power allocated to $x_l$ must satisfy:

(11)

$$\begin{array}{}\text{(11)}& 0\le P_l^{MU}\le P_{max,l}^{MU}.\end{array}$$

If at the same time the $m^{th}$ D2D transmitter is sending signal to its pair:

(12)

$$\begin{array}{}\text{(12)}& 0\le P_{l,m}^{D2D}\le P_{max,l}^{D2D},\end{array}$$

where $P_{max,l}^{MU/D2D}$ is maximum power that can be allocated and $P_l^{MU/D2D}$ is allocated power to MU/D2D.

From Equations (11) and (12), the achievable rates of MU and D2D users can be calculated. In $f^{th}$ slot, the total sum rate is rate of MU and the data rate of D2D scheduled for communication:

(13)

$$\begin{array}{}\text{(13)}& R_{total}(f)=\sum _{m=1}^M\sum _{f=1}^F{b}_m(f)R\text{'}(f)/t_s+R_{MU}(f),\end{array}$$

where $R_{MU}(f)$ denotes the sum rate of MU in $f^{th}$ slot, $b_m(f)$ is Boolean variable: ‘1’indicates $m^{th}$ user is scheduled in $f^{th}$ slot.

In the slot, a scheduled transmitter can adjust its transmit power to achieve maximum throughput while keeping latency limitations into consideration of D2D users. The time division multiple access (TDMA) is used for scheduling in each slot for D2D users that maximizes the sum rate of the network (queuing time or latency is also considered).

Simulation results

To evaluate the performance with respect to latency consideration, F consecutive frames are analyzed. The D2D implementation strategy and previous frame decides the adopted solution. Three parameters are analyzed for evaluation of performance for four different scenarios of D2D implementation.

Parameters

1. Latency of mobile user: The latency experience by a mobile user depends upon the latency of D2D pair that experiences maximum latency for F frames:

   (14)

   $$\begin{array}{}\text{(14)}& t_{max}=\max (t_{MU}(f)),1\le f\le F\end{array}$$

2. Power efficiency: Power efficiency is defined as the mean of power consumption required for achieving needed spectral efficiency:

   (15)

   $$\begin{array}{}\text{(15)}& P_e=\frac{{\sum }_{m=1}^M{R}_m^{\text{'}}/t_s}{BW\times {\sum }_{m=1}^M{a}_m{P}_s}\end{array}$$

3. Cumulative distributed function (CDF) of mean total sum throughput that is equal to:

(16)

$$\begin{array}{}\text{(16)}& R_{mean}=\frac{{\sum }_{f=1}^F{R}_{total}(f)}{F}\end{array}$$

The four scenarios are:

1. Minimum rate requirement for MU and power is variable (MRR).

2. No minimum rate requirement for MU and power is variable (NMRR).

3. Minimum rate requirement for MU and power is maximum (MRR-Pmax).

4. No minimum rate requirement for MU and power is maximum (NMRR-Pmax).

Figure 1 compares the latency of MU in presence of D2D pairs. The MU experience minimum latency when minimum rate requirement is defined, i.e. For MRR and MRR-Pmax. The variable power and no minimum rate for MU (NMRR) experiences maximum latency. The power efficiency $P_e$ is approximately equal to 4.0, 4.75, 0.58, and 0.65 for MRR, NMRR, MRR-Pmax, and NMRR-Pmax, respectively.

Figure 1:

Figure 2 compares the data rate supported in four scenarios. The data rates taken are from 0 to 12 Mbps. When the power is set to maximum, the 50% of data rates that can be supported are less than 2 Mbps. When the power is variable the supported around 65% data rate is around 5 Mbps. When data rate is below 5 Mbps, the ratio of lower data rate users is relatively on higher side that makes CDF curve to experie nce a slower increase while at higher data rate the case is exactly opposite that makes CDF to increase rapidly. The cumulative distribution for throughput sum gives poor results for variable power scenarios as compare to maximum power scenarios. Also, among variable power and maximum power scenarios, the scenario without minimum rate requirements performs better.

Figure 2:

Conclusion

The work in this paper focuses on sharing of the uplink resources of mobile user with D2D pairs using both NOMA-based power allocation and TDMA-based slot sharing. The work is interference and latency driven. For four different scenarios, latency, data rate, power efficie ncy, and throughput are compared. The results show that when power is maximized and fixed, higher throughput and lower latency can be achie ved as compared to scenarios when power is variable. The advantages associated with variable power scenarios are better power efficie ncy and better support for data rates.

SINR	Signal to interference plus noise ratio
D2D	Device to device
MU	Mobile user
Rc	Data rate of channel
${\sigma }^2$	Variance of Additive White Gaussian Noise (AWGN)
R and TH	Rate and throughput
${\lambda }_m$	Data arrival at D2D transmitter
Q	Queue length