Power Allocation Intelligent Optimization for Mobile NOMA Communication System

Abstract

Non-orthogonal multiple access (NOMA) technology can greatly improve user access and spectral efficiency. This paper considers the power allocation optimization problem of a two-user mobile NOMA communication system. Firstly, a mobile NOMA communication system model is established. Then, we analyze the outage probability (OP) of mobile NOMA communication system and the relationship between OP performance and user power allocation coefficient. Finally, the optimization objective function is established, and a power allocation optimization algorithm employing monarch butterfly optimization (MBO) is proposed. Compared with firefly algorithm and artificial fish swarm algorithm, the efficiency of MBO algorithm is increased by 20.7%, which can better improve the OP performance.

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1. Introduction

Recently, the number of mobile users has increased rapidly. With the rapid growth of wireless communication data, the available spectrum becomes more and more crowded, and the space in the electromagnetic spectrum will become more and more scarce [1]. To meet the high-quality communication and large-scale user access, 5G mobile communication technology has attracted extensive attention [2]. 5G mobile communication technology has been rapidly popularized with ultrahigh bandwidth, ultralarge capacity, ultralow delay, and ultrasmall energy consumption, which has brought far-reaching impact and change to people's life, work, and national economic development [3, 4].

Non-orthogonal multiple access (NOMA) technology has good fairness and considerable spectral efficiency, and it is regarded as a key technology of 5G mobile communication [5–7]. A novel deep learning method was proposed to cut down the computation complexity of NOMA multiuser detection in [8]. In [9], a multiagent deep learning method was proposed to solve the complex NOMA optimization problem, which considered user fairness and decoding complexity. The authors in [10] proposed a trusted NOMA model and maximized the secure rate at the near user by using KKT conditions. To improve the NOMA system performance, the authors in [11] proposed a joint queue-aware and channel-aware scheduling to reduce traffic delay.

Power allocation can improve the NOMA performance in [12–14]. The authors in [15] constructed a multicarrier NOMA system and proposed a power allocation algorithm to reduce computational complexity. In [16], considering an unmanned aerial vehicle (UAV)-assisted NOMA system, user grouping and power allocation were used to reduce the relative distance between users and UAV. The authors in [17] obtained the error probability to fairly allocate power to different users of the NOMA system. Considering vehicle mobility, the authors in [18] proposed a sequence-based power allocation algorithm for NOMA UAV-aided vehicular platooning. However, there are some problems in these schemes, such as large amount of calculation, poor energy efficiency performance, insufficient power utilization, and unable to balance the fairness and service quality of users.

In order to obtain the best power allocation coefficient, the swarm intelligence optimization algorithm has been widely used in [19, 20]. In [21], artificial fish swarm algorithm (AFSA) optimized a wireless sensor network coverage problem, which can reduce the energy consumption. With simplified propagation and firefly algorithm (FA), an improved power point tracking algorithm was proposed in [22]. An improved cuckoo search algorithm was proposed to optimize the mobile outage probability (OP) prediction in [23]. However, these algorithms still have some shortcomings, such as low discovery rate, slow solution speed, and low solution accuracy.

Therefore, we investigate the mobile power allocation optimization. The main contributions of this paper are as follows:

(1) A mobile NOMA communication system model is established. For ideal communication conditions, we derive the exact expressions for OP and analyze the relationship between OP and power allocation coefficient.

(2) Considering the system efficiency and user fairness, we have established the optimization objective function. Employing monarch butterfly optimization (MBO), an intelligent optimization algorithm is proposed. MBO can reduce the computing parameters. The power allocation optimization algorithm employing MBO has good convergence performance and optimization performance.

(3) Compared with FA and AFSA, the MBO algorithm can obtain the shortest time, which is 18.7063s, while AFSA is 48.9128s, and FA is 23.6096s. The efficiency of MBO is increased by 20.7%, which can better improve the OP performance of the mobile NOMA system.

2. System Model

Figure 1 is the mobile NOMA communication system. The system is composed of a source S, a far user Df, and a near user Dn. h_i represents the channel gains of S ⟶ Df and S ⟶ Dn, $i=SDn,SDf$. h_i is expressed as follows [24]:$$\begin{array}{}\text{(1)}& h={\displaystyle \prod _{t=1}^N{a}_t},\end{array}$$where a_t is a Nakagami variable.

[figure(s) omitted; refer to PDF]

S transmits $\sqrt{a_1{P}_{\text{s}}}{x}_1+\sqrt{a_2{P}_{\text{s}}}{x}_2$ to Df and Dn. P_s is the transmission power. a₁ and a₂ are power allocation coefficients of Df and Dn, respectively. $a_1+a_2=1$, and $a_1>a_2$.

The signals received at Df and Dn are as follows [25, 26]:$$\begin{array}{c}\text{(2)}& y_{\text{Df}}=h_{\text{SDf}}\sqrt{a_1{P}_{\text{s}}}{x}_1+\sqrt{a_2{P}_{\text{s}}}{x}_2+{\eta }_{\text{SDf}}+{\nu }_{\text{SDf}},y_{\text{Dn}}=h_{\text{SDn}}\sqrt{a_1{P}_{\text{s}}}{x}_1+\sqrt{a_2{P}_{\text{s}}}{x}_2+{\eta }_{\text{SDn}}+{\nu }_{\text{SDn}},\end{array}$$where ${\nu }_{SDf}$ and ${\nu }_{SDn}$ are AWGN of Df and Dn, respectively, and ${\eta }_{SDf}$ and ${\eta }_{SDn}$ are the distortion noise from the transmitter.

The signal-to-interference noise ratios of Df and Dn are as follows [25, 26]:$$\begin{array}{c}\text{(3)}& {\gamma }_{\text{SDn}}=\frac{{h_{\text{SDn}}}^2{a}_2\gamma }{{h_{\text{SDn}}}^2\gamma +\gamma +1},{\gamma }_{\text{SDf}}=\frac{{h_{\text{SDf}}}^2{a}_1\gamma }{{h_{\text{SDf}}}^2{a}_2\gamma +\gamma +1},\\ {\gamma }_{\text{SDf}}=\frac{{h_{\text{SDf}}}^2{a}_1\gamma }{{h_{\text{SDf}}}^2{a}_2\gamma +\gamma +1},\end{array}$$where $\gamma =P_{\text{s}}/N_0$ is the transmit signal-to-noise (SNR) ratio at S.

3. OP Performance Analysis

3.1. OP of Df

The OP of Df is expressed as$$\begin{array}{c}\text{(4)}& {\text{OP}}_{\text{Df}}=\mathrm{Pr}{\gamma }_{\text{SDf}}<{\gamma }_{\text{thf}}=\mathrm{Pr}\frac{{h_{\text{SDf}}}^2{a}_1\gamma }{{h_{\text{SDf}}}^2{a}_2\gamma +\gamma +1}<{\gamma }_{\text{thf}}\\ =\mathrm{Pr}{h_{\text{SDf}}}^2<\frac{\gamma +1{\gamma }_{\text{thf}}}{a_1\gamma -a_2\gamma {\gamma }_{\text{thf}}}\\ ={\displaystyle {\int }_{\text{0}}^{\gamma +1{\gamma }_{\text{thf}}/a_1\gamma -a_2\gamma {\gamma }_{\text{thf}}}{f}_{{h_{SDf}}^2}y\text{d}y}\\ =F_{{h_{\text{SDf}}}^2}y|{}_{\text{0}}^{\gamma +1{\gamma }_{\text{thf}}/a_1\gamma -a_2\gamma {\gamma }_{\text{thf}}}\\ =G_{\mathrm{1,3}}^{\mathrm{2,1}}\frac{\gamma +1{\gamma }_{\text{thf}}}{a_1\gamma -a_2\gamma {\gamma }_{\text{thf}}}|{}_{1\text{,}\mathrm{....}\text{,}\mathrm{1,0}}^1,\end{array}$$where ${\gamma }_{\text{thf}}$ is the interrupt threshold of Df.

3.2. OP of Dn

The OP of Dn is given as$$\begin{array}{c}\text{(5)}& {\text{OP}}_{\text{Dn}}=\text{Pr}{\gamma }_{\text{SDf}⟶\text{n}}<{\gamma }_{\text{thf}}\text{,}{\gamma }_{\text{SDn}}<{\gamma }_{\text{thn}}=\text{Pr}{h_{\text{SDn}}}^2<\frac{\gamma +1{\gamma }_{\text{thf}}}{a_1\gamma -a_2\gamma {\gamma }_{\text{thf}}}\text{,}{h_{\text{SDn}}}^2<\frac{\gamma +1{\gamma }_{\text{thn}}}{a_2\gamma -\gamma {\gamma }_{\text{thn}}},\end{array}$$where ${\gamma }_{\text{thn}}$ is the interrupt threshold of Dn.

To simplify the integration process, we define the following variables:$$\begin{array}{c}\text{(6)}& {\tau }_1=\frac{\gamma +1{\gamma }_{\text{thf}}}{a_1\gamma -a_2\gamma {\gamma }_{\text{thf}}},{\tau }_2=\frac{\gamma +1{\gamma }_{\text{thn}}}{a_2\gamma -\gamma {\gamma }_{\text{thn}}},\\ \tau =\text{max}{\tau }_1,{\tau }_2.\end{array}$$

Bringing the above variables into (11), we obtain that$$\begin{array}{c}\text{(7)}& {\text{OP}}_{\text{Dn}}=\text{Pr}{h_{\text{SDn}}}^2<{\tau }_1\text{,}{h_{\text{SDn}}}^2<{\tau }_2=\text{Pr}{h_{\text{SDn}}}^2<\text{max}{\tau }_1,{\tau }_2\\ =\text{Pr}{h_{\text{SDn}}}^2<\tau \\ =F_{{h_{\text{SDn}}}^2}{y|}_0^{\tau }\\ =G_{\mathrm{1,3}}^{\mathrm{2,1}}{\tau |}_{1,\dots ,\mathrm{1,0}}^1.\end{array}$$

4. Intelligent Power Allocation Optimization Employing MBO Algorithm

Here, we employ the MBO algorithm to optimize the mobile power allocation.

4.1. Optimization Objective Function

To achieve high efficiency and user fairness, we should ensure $\min {\text{OP}}_{\text{Df}}+{\text{OP}}_{\text{Dn}}$ and $\text{min}{\text{OP}}_{\text{Df}}{-\text{OP}}_{\text{Dn}}$. Therefore, the optimization objective function is$$\begin{array}{}\text{(8)}& \min \begin{array}{c}{G}_{\mathrm{1,3}}^{\mathrm{2,1}}{\frac{\gamma +1{\gamma }_{\text{thf}}}{a_1\gamma -a_2\gamma {\gamma }_{\text{thf}}}|}_{1\text{,…,}\mathrm{1,0}}^1+G_{\mathrm{1,3}}^{\mathrm{2,1}}{\tau |}_{1,\text{…},\mathrm{1,0}}^1+\\ G_{\mathrm{1,3}}^{\mathrm{2,1}}{\frac{\gamma +1{\gamma }_{\text{thf}}}{a_1\gamma -a_2\gamma {\gamma }_{\text{thf}}}|}_{1\text{,…,}\mathrm{1,0}}^1-G_{\mathrm{1,3}}^{\mathrm{2,1}}{\tau |}_{1,\text{…},\mathrm{1,0}}^1\end{array}.\end{array}$$

4.2. MBO Intelligent Optimization Algorithm

Therefore, employing the MBO algorithm, an intelligent power allocation optimization algorithm is proposed. In [27], it presents the MBO algorithm.

4.2.1. Population Initialization

The number of the monarch butterfly population is N. The number of iterations is MaxGen, and the adjustment rate is BAR.

4.2.2. Fitness Evaluation

The fitness value of each monarch butterfly individual is calculated and sorted. The sorted population is divided into two subpopulations NP₁ and NP₂, respectively. They have N₁ and N₂ individuals, respectively.

4.2.3. New Subpopulation Generation

At the current iteration t, the NP₁ and NP₂ generate two new subpopulations, respectively. For NP₁, it uses the migration operator to generate a new subpopulation, which is expressed as follows:$$\begin{array}{}\text{(9)}& \begin{array}{cc}{x}_{i,k}^{t+1}=x_{r_1,k}^t,& r\le p,\\ x_{i,k}^{t+1}=x_{r_2,k}^t,& \text{else,}\end{array}\end{array}$$where x_r1 and x_r2 represent the kth element of r₁ and r₂ that is the newly generated position of r₁ and r₂, respectively. r₁ and r₂ are randomly selected from NP₁ and NP₂, respectively. r is a random number.

For NP₂, it uses the adjustment operator to generate a new subpopulation, which is expressed as follows:$$\begin{array}{}\text{(10)}& \begin{array}{cc}{x}_{i,k}^{t+1}=x_{\text{best},k}^t,& r\le p,\\ x_{i,k}^{t+1}=x_{r3,k}^t,& \text{else,}\end{array}\end{array}$$where x_best represents the position of the globally optimal individual and x_r3 represents the location of r₃, which is randomly selected from NP₂.

rand is between [0, 1]. If rand>BAR, NP₂ updates $x_{i,k}^{t+1}$ again. The process is as follows:$$\begin{array}{}\text{(11)}& \begin{array}{c}{x}_{i,k}^{t+1}=x_{i,k}^t+\beta \ast \text{d}{x}_k-0.5,\\ \text{d}x=\text{Levy}{x}_i^{t+1},\end{array}\end{array}$$where β is the weight factor and dx represents the step size which is calculated by the Levy function.

4.2.4. New Subpopulation Mergence

It merges the two newly generated subpopulations and calculates the fitness of the new population. Repeat above process, and when the number of iterations reaches MaxGen, the best solution is obtained.

5. Performance Analysis

This section will analyze the OP performance and optimize the power allocation using MBO, AFSA, and FA algorithms.

Table 1 gives the simulation parameters. For the ideal case, the residual hardware impairment k = 0, and the incomplete channel state information $\sigma =0$. Figure 2 shows the OP performance with different m. From Figure 2, when the power allocation coefficient is constant, the system OP performance becomes better with the increase in SNR and m. The OP performance with different N is shown in Figure 3. As N is decreased, it can minimize the system OP.

Table 1

Simulation parameters.

Parameter	Value
K	0
$\sigma$	0
M	1, 2, 3, 4
N	1, 2, 3, 4

[figure(s) omitted; refer to PDF]

We select four test functions, which are shown in Table 2. Figure 4 shows the convergence performance of different algorithms. For F₁–F₄ functions, the MBO is the best.

Table 2

Four test functions.

	Function	Ranges	Dimension
Griewank	$\text{F}1={\displaystyle {\sum }_{i=1}^d{x}_i^2/4000-}{\displaystyle {\prod }_{i=1}^d\cos x_i/\sqrt{i}+1}$	[−600, 600]	20
Rastrigin	$\text{F}2=10d+{\displaystyle {\sum }_{i=1}^d{x}_i{}^2-10\cos 2\pi x_i}$	[−5.12, 5.12]	20
Sphere	$\text{F}3={\displaystyle {\sum }_{i=1}^d{x}_i{}^2}$	[−500, 500]	20
Schwefel	$\text{F}4=418.9828d-{\displaystyle {\sum }_{i=1}^d{x}_i\sin \sqrt{x_i}}$	[−500, 500]	20

[figure(s) omitted; refer to PDF]

Next, the power allocation will be optimized by MBO, FA, and AFSA. Table 3 shows the simulation parameters for power allocation. Table 4 shows the power allocation optimization comparison of MBO, FA, and AFSA algorithms. Compared with FA, MBO has a 20.7% decrease. The iterative optimization process of the MBO, FA, and AFSA algorithms is shown in Figure 5.

Table 3

Simulation parameters for power allocation.

Parameter	Value
Iteration	1000
Population number	100
Dimension	1
Range	[0.5, 0.9]

Table 4

Power allocation optimization comparison.

	Optimal power allocation coefficient	Time (s)
MBO	0.56768	18.7063
FA	0.56768	23.6096
AFSA	0.56768	48.9128

[figure(s) omitted; refer to PDF]

The system performance comparison of the MBO, FA, and AFSA algorithms is shown in Figure 6. From Figure 6, the performance of the MBO algorithm is good, which is the same as FA and AFSA algorithms. However, the MBO algorithm has a low complexity.

[figure(s) omitted; refer to PDF]

6. Conclusion

This paper studies the power allocation optimization for the mobile NOMA communication system. Firstly, the mobile NOMA model is built, and the OP expressions for Df and Dn are derived. Then, the optimization objective function is established, and a power allocation optimization algorithm is proposed. Finally, it can obtain the best power allocation coefficient. The efficiency of the MBO algorithm is improved by 20.7%.

Acknowledgments

This project was supported by the National Natural Science Foundation of China (No. 11664043).

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