Computational-Intelligence-Based Spectrum-Sharing Scheme for NOMA-Based Cognitive Radio Networks

Abstract

The integration of non-orthogonal multiple access (NOMA) technology and cognitive radio networks (CRNs) promises to enhance the spectrum utilization efficiency of 5G and beyond-5G (B5G) mobile communication systems. In this article, a NOMA-based spectrum-sharing scheme is proposed for dual-hop CRNs in which a primary transmitter separated by a long distance from the primary receiver communicates via NOMA-based CRN. In this scenario, we mathematically formulate a constrained optimization problem to maximize the sum rate of all secondary users (SUs) while maintaining the total transmit power of the system. Inspired by the effectiveness of computational intelligence (CI) tools in solving non-linear optimization problems, this article proposes three CI-based solutions to the given problem aiming to guarantee quality of service (QoS) for all users. In addition, an enhanced version of the classic artificial bee colony (ABC) algorithm, referred to here as the enhanced-artificial-bee-colony (EABC)-based power allocation scheme, is proposed to overcome the limitations of classic ABC. The comparison of different CI approaches illustrates that the minimum power required by the secondary NOMA relay to satisfy the primary rate threshold of 5 bit/s/Hz is 20 mW for EABC, while ABC, PSO and GA achieve the same target at 23 mW, 27 mW and 32 mW, respectively. Thus, EABC reduces power consumption by 13.95% compared to ABC, while 29.78% and 46.15% power-saving is achieved compared to PSO and GA, respectively.

1. Introduction

The rapid development of wireless communication and the resulting unprecedented growth rate of interconnected wireless devices bring challenges for 5G and Beyond 5G (B5G) mobile systems, such as shortage of spectrum resources, spectrum utilization efficiency, mobility, user fairness and so on [1]. In order to cope with these challenges, several candidate technologies have been suggested in recent years. However, a single technology may not be able to satisfy the performance goals of next-generation wireless networks, thus demanding the integration of multiple technologies [2]. Among various potential technologies of the future, cognitive radio (CR) and non-orthogonal multiple access (NOMA) are two primary techniques for enhancing spectrum utilization efficiency [3].

The principal idea behind cognitive radio networks (CRNs) is to offer higher spectral efficiency by enabling the coexistence of primary users (PUs) and secondary users (SUs) using dynamic spectrum access techniques [4]. The fundamental spectrum-sharing modes in CRNs are underlay, overlay and interweave [5,6]. In underlay mode, SUs transmit simultaneously with the PU on the same time slot and frequency as long as the interference caused for the PU stays within tolerable limits. Overlay is another spectrum-sharing paradigm in CRNs in which SUs acquire a priori knowledge of the PU’s signal and relay the PU’s message while simultaneously transmitting their own message. Such cooperative spectrum sharing via the secondary relay offers an increased data rate for the SU and better reliability of data detection for the PU. In a coexistence scenario of multiple potential SUs, the primary network tends to select the best secondary relay for cooperation to achieve the maximum possible advantage. In interweave mode, also known as opportunistic spectrum access, SUs employ spectrum-sensing techniques for the detection of spectrum holes and transmit only if the PU is absent.

Recently, NOMA has emerged as an attractive technology for serving a massive number of users by multiplexing in the power domain over the same code/time/frequency [7]. For this purpose, NOMA employs a combination of superposition coding (SC) and successive interference cancellation (SIC) to retrieve the multiplexed signals [8]. Unlike conventional multiple access techniques, NOMA improves user fairness and meets quality-of-service (QoS) requirements through dynamic resource allocation, i.e., by allocating more power to users operating at long distances or having poor channel conditions to achieve the desired total throughput [9]. Integrating cooperative diversity with these two competent technologies, i.e., CR and NOMA, can further enhance communication reliability and system capacity [10].

In the domain of numerical optimization, computational intelligence (CI), commonly defined as soft computing, is a part of computer and engineering sciences that consists of a set of nature-inspired computational methods to address real-world data-driven problems. The motivation behind CI-based techniques is to apply a heuristic approach of perception and control for processing complex data sources under uncertain environmental conditions. The CI-based methods are regarded as “intelligent” methods that offer better results than conventional methods such as regression methods [11]. During the last two decades, various CI techniques have been extensively applied to diverse optimization problems ranging from industrial applications to complex scientific research problems [12].

The three core components that exist under the umbrella of CI are fuzzy logic (FL), artificial neural networks (ANN), and evolutionary algorithms (EA). Among these, EAs are inspired by the collective intelligence of natural systems and the biological principle of selection to solve numerical optimization problems using different approaches such as genetic programming and swarm intelligence. Since our optimization problem has a nonlinear objective function and constraints, we take advantage of the random and derivative-free nature of metaheuristics from the domain of CI to achieve the best global solution to the problem.

Among the most popular and state-of-the-art EA techniques are genetic algorithms (GA), introduced by Holland in 1975 [13], particle swarm optimization (PSO), developed by Kennedy and Eberhart in 1995 [14], and the artificial bee colony (ABC) algorithm proposed by Dervis Karaboga in 2005 [15]. ABC follows the foraging behavior of honey bee swarms, PSO is motivated by the social behavior of a bird flock or fish school, and GA is inspired by the Darwinian theory of natural selection. These three derivative-free global optimizers are well-established to address complex real-world problems. Basically, these algorithms operate recursively on a population of solutions in a randomly guided manner and provide effective alternative search strategies in situations in which traditional mathematical models do not apply. A potential or candidate solution is referred to as a food source in ABC, a particle in PSO, and a chromosome in GA. These versatile tools and their variants have been extensively applied to solve diverse optimization problems. Some of their prominent applications in CRNs include [16,17] for GA, [18,19] for PSO, and [20,21] for ABC.

1.1. Related Work

The overlay scenario of NOMA-based CRNs presents a promising combination for improving spectrum utilization efficiency, in which a SU relays the PU’s signal and as a reward transmits its own signal simultaneously using the NOMA principle. In [22], the authors investigated a cooperative spectrum-sharing scheme in which a secondary transmitter assisted the primary transmission as a relay. In exchange for cooperation, the secondary transmitter employed the NOMA transmission policy and was able to transmit simultaneously with the PU over the same subchannel. Another NOMA-assisted cooperative transmission scheme was proposed for CRNs [23]. It was shown that by applying cooperative transmission in a downlink overlay scenario, diversity gains were achieved for both PU and SU.

Kader proposed a NOMA-based overlay spectrum-sharing protocol over independent Rayleigh fading channels [24]. In order to enhance spectrum utilization efficiency and system capacity, the proposed scheme involved coordinated direct and relayed transmission through a secondary transmitter acting as a relay to assist a weak PU in its communication. Performance analysis in terms of ergodic sum capacity and outage probability (OP) showed superior performance of the proposed cooperative spectrum-sharing-based NOMA transmission over conventional NOMA-based communication.

In [25], a multiple-user NOMA-based CRN is investigated that has an overlay scenario in which a single best SU is selected based on signal-to-noise ratio (SNR) to assist the primary communication. The performance of the proposed system is investigated through OP and capacity analysis for both primary and secondary networks. Yet another cooperative spectrum-sharing strategy exploiting NOMA in the second time slot was proposed by Chen et al. in reference [26], in which a secondary transmitter relays the primary information concurrently with its own transmission.

In another NOMA-based spectrum-sharing protocol for overlay CRNs [27], spatial modulation at the secondary relay is incorporated with antenna selection to enable simultaneous transmission to primary and secondary receivers. The authors showed through simulations that NOMA with spatial modulation significantly improved spectrum utilization efficiency with reduced detection complexity. In another NOMA-aided spectrum-sharing scheme for multicast overlay CRNs [28], the communication process is completed in three phases. In the first phase, a common base station serves both primary and secondary networks using the NOMA principle, while SUs relay the PU’s signal in the second phase to overcome fading impairments. As an incentive, the third phase is dedicated to supporting the multicast of the SUs over the PU’s licensed spectrum. The derived analytical expressions and simulation results showed improved outage performance of SUs while securing the primary user’s QoS requirements.

Nam-Soo Kim proposed a CR NOMA system for the performance enhancement of both primary and secondary networks with a primary direct link (DL) and relay selection [29]. The performance of the primary network is improved by combining technologies, whereas channel-state-information (CSI)-based relay selection is performed on the secondary network to offer spatial diversity. Zhang et al. proved that cooperative NOMA-based overlay cognitive terrestrial networks show superior performance to traditional OMA networks [30]. All these research contributions highlight that combining overlay CRNs with cooperative NOMA under the Rayleigh channel model holds tremendous potential for improving spectrum utilization efficiency.

To further elaborate on the contributions of this article, the features of existing contributions on NOMA-based CRNs for Rayleigh fading channels are summarized in

Table 1. Summary of Existing Works.

Ref.	Year	Major Focus	Primary DL	Performance Analysis
[22]	2018	Single cooperative relay to assist distant PU	Yes	OP and ergodic sum capacity showed improved performance compared to conventional NOMA networks
[23]	2016	Select the single best relay to forward the primary signal	Yes	Improved OP, but not suitable for long physical separation between primary transmit-receive pair
[24]	2020	Coordinate direct and secondary relay transmission to assist weak PU	Yes	OP and ergodic sum capacity analysis through Monte Carlo simulations showed improved performance compared to conventional NOMA networks
[25]	2022	Direct and relay transmission to assist cell-edge users	Yes	Better SIC and more accurate CSI required to enhance OP and system capacity
[26]	2018	Enable primary communication through relay selection and power control	No	Improved secondary transmission rate and total transmit power of the system, but fairness among SRs is ignored
[27]	2018	Utilize NOMA with spatial modulation and antenna selection	Yes	Symbol error probability analysis through Monte Carlo simulations showed improved spectrum utilization efficiency, but more multifaceted
[28]	2018	Exploit spatial diversity to overcome fading impairments	Yes	Improved OP and ergodic capacity provided appropriate allocation of time slots for cooperation
[29]	2020	Exploit spatial diversity through relay selection and combining technologies	Yes	Improved OP and reduced transmit power with increase in the number of SUs as compared to conventional CR NOMA networks, but performance depends on location of the relay
-	This Article	Enable primary communication under deep shadowing through secondary NOMA relay and single best SU from secondary network to exploit spatial diversity	No	Optimize the sum rate of SUs and total transmit power of the system using different state-of-the-art CI tools (EABC, ABC, GA, and PSO) while guaranteeing QoS at the primary network

, while highlighting the benefits of this study. We can observe that none of these contributions presents a CI-based solution for maximizing the sum rate of the NOMA-based secondary network by optimizing overall system transmit power while guaranteeing the QoS requirement of the primary network. This article aims to fill this research gap by presenting the following contributions.

1.2. Contributions

In this article, owing to the overlay approach of a truly win-win situation for both primary and secondary networks, a NOMA-assisted power-domain cooperative overlay spectrum-sharing framework is developed for downlink transmission in CRNs. In the proposed scheme, the information for the PU in the absence of DL is retransmitted through the SU selected from the secondary network, in addition to the secondary NOMA relay. The main contributions of this work are as follows.

• For a dual-hop downlink CRN operating in half-duplex mode, a novel NOMA-assisted spectrum-sharing scheme is proposed in which a secondary NOMA relay (SR) first transmits the information for the PU and multiple SUs to the corresponding destinations. Then, a single best SU retransmits the primary signal in order to enhance QoS using maximal ratio combining (MRC), while the primary base station (PBS) transmits the next frame for the PU to the SR at the same time. The SU selection is based on the best channel condition for the PU.
• For the implementation of the proposed scheme, an enhanced version of ABC, referred to here as the enhanced-artificial-bee-colony (EABC)-based power allocation scheme, is proposed to overcome the limitations of classic ABC.
• To validate the effectiveness of the proposed EABC-based scheme, its performance is compared with the classic ABC and with the existing competent EA-based techniques in the literature, i.e., GA and PSO. It is clearly observed through simulations that EABC outsmarts the traditional version and other global optimizers in terms of convergence time and in achieving a higher sum rate while consuming minimum transmit power.
• The performance of the proposed scheme is validated by varying the transmit power at the NOMA relay, the rate threshold of the PU, and the number of SUs.

Thus, the proposed scheme not only enables communication between distant primary terminals but saves the total transmit power of the system as well.

1.3. Organization and Notations

The rest of the article is structured as follows. Section 2 explains the system model and the related assumptions for the mathematical formulation of the optimization problem. CI-based power allocation schemes to solve the problem at hand are discussed in Section 3. Section 4 presents the simulation results, while Section 5 concludes the article. For convenience, a list of notations is provided in

Table 2. Notations.

Notation	Definition
SUk	kth secondary user
SUsel	Selected SU for retransmission of xQ
Γ	Set of potential SUs
K	Number of potential SUs
Q	Primary Receiver
x0	Signal required by Q
xk	Signal required by SUk
xSR	Signal received by SR
xI	Composite signal transmitted by SR
g0	Link gain between SR and Q
gk	Link gain between SR and SUk
h0	Link gain between PBS and SR
hk	Link gain between SUk and Q
hsel	Link gain between SUsel and Q
P0	Transmit power of PBS allocated to Q
PS	Transmit power of SR
pk	Power allocated to SUk
Psel	Transmit power of SUsel
γ0	Rate threshold required by Q
γk	Rate threshold required by SUk
λ0	Power allocation coefficient of Q
λk	Power allocation coefficient of SUk
Rp	Achievable rate at SR
Rk	Achievable rate at SUk
RQ	Achievable rate at Q
σ2	Noise variance
$\rho$	Probability of fitness

.

2. System Model and Problem Formulation

Consider a dual-hop cooperative spectrum-sharing network as shown in Figure 1, consisting of primary and secondary networks. The primary network comprises a primary base station (PBS) and a primary receiver Q, whereas the secondary network consists of a set of K potential secondary users $\mathsf{\Gamma }={\left\{S{U}_k\right\}}_{k=1}^K$ and a NOMA-based secondary relay SR. All the channels follow Rayleigh block fading. The signals required by Q and SU_k are denoted by x₀ and x_k, respectively. The DL between the primary transmit-receive pair is absent due to deep shadowing, as a result of which the PBS receives assistance from the SR to reach its intended receiver Q. In addition, one best SU from the set of potential SUs, i.e., SU_sel, is selected to retransmit the primary signal x₀ to Q. In this scenario, NOMA being a combination of SIC and SC techniques is the best choice for simultaneously transmitting the primary and secondary signals. In the overlay scenario of CRNs, the NOMA-based secondary relay has the potential to enhance the performance of the primary network in shadowing areas and provide high spectral efficiency. NOMA ensures user fairness through variable power allocation, taking into consideration the distance between the transmit-receive pair and the channel conditions. Thus, users at long distances or having poor channel conditions are allocated more power to achieve the desired total throughput.

Without loss of generality, the following assumptions are made.

• Each node is equipped with a single antenna and thus operates in a half-duplex mode.
• Distance between SR and Q is greater than the distance between SR and any k^th SU, hence the channel gains are arranged in the order of |$g_0$| ≤ |$g_1$| ≤ … ≤ |$g_K$|.
• The whole communication process is controlled by NOMA relay SR with necessary control signals.
• Background noise is modeled as Additive White Gaussian Noise (AWGN) with zero mean and variance σ².

2.1. NOMA-Assisted Power Allocation Scheme

In the proposed NOMA-assisted transmit power allocation scheme, the whole communication process is divided into two time slots. First, information for the PBS and all SUs is transmitted via the NOMA relay SR to the destinations. Then, one best SU retransmits the PBS’s signal while the SR simultaneously receives the information for the PBS for the next time slot. In the proposed scheme, MRC is employed to guarantee reliable transmission of the primary signal, which improves the QoS of the system. The above communication process is illustrated in Figure 2 and explained in further detail below.

2.1.1. Time Slot 1

In time slot 1, we can select the best receiver SU_sel from the potential SUs based on the channel gain to retransmit the decoded signal to the user Q. The criteria for the selection of the SU can be mathematically expressed as $k^{\ast }=arg\underset{k^{\ast }\in \mathsf{\Gamma }}{\max }{\left|h_k\right|}^2$. The selected SU will re-transmit $x_0$ of the previous frame to Q. Simultaneously, PBS transmits x₀ of the current frame to the SR. Here it is important to mention that we develop a NOMA-assisted cooperative overlay spectrum-sharing framework comprising a primary transmission phase and a secondary transmission phase. Therefore, the SR can perfectly eliminate $x_0$ of the previous frame after successful decoding and local caching. Thus, during the primary transmission phase, the signal received at the SR can be mathematically expressed as [31]:

$$x_{SR}=\sqrt{P_0}{h}_0{x}_0+n_{SR}$$

(1)

where $n_{SR}$ is AWGN observed at the SR. From Equation (1), the achievable rate at the SR can be mathematically expressed as:

$$R_P=lo{g}_2\left(1+\frac{P_0{\left|h_0\right|}^2}{{\sigma }^2}\right)$$

(2)

where, $\frac{P_0}{{\sigma }^2}$ is the transmit SNR. For successful decoding of $x_0$ at the SR, the above rate should satisfy

$$R_P\ge {\gamma }_0$$

(3)

The corresponding minimum transmit power required at the PBS to achieve this rate can easily be obtained as:

$$P_0\ge {\sigma }^2\left(\frac{2^{{\gamma }_0}-1}{{\left|h_0\right|}^2}\right)$$

(4)

Finally, the distance between the PBS and the SR is kept sufficiently large to guarantee the successful transmission of $x_0$.

2.1.2. Time Slot 2

During time slot 2, the SR will transmit the superimposed signal $x_I$ for all SUs and the user Q, which can be expressed as $x_I=\sum _{k=0}^K\sqrt{p_k{x}_k}$. For k = 0, the intended signal is for the primary network.

For k = 1, 2, … K, the intended signal is for the secondary receivers.

Based on the above assumption, i.e., |$g_0$| ≤ |$g_1$| ≤ … ≤ |$g_K$|, we can set $p_0\ge p_1\ge \dots \ge p_K\ge 0$ such that, $\sum _{k=0}^K{p}_k=P_S$. Applying the NOMA principle, we define the power allocation coefficient ${\lambda }_k=\frac{{\left|g_k\right|}^2}{{\sigma }^2}$ which clearly means that $0\le {\lambda }_0\le {\lambda }_1\le \dots \le {\lambda }_K$. Each receiving node applies SIC to decode the weaker signals directly. It is assumed that if $S{U}_1$ having the poorest channel condition towards Q can decode $x_0$ successfully, then the remaining SUs can also decode $x_0$. Mathematically, we can express this condition as $R_{x_0\to 1}\ge {\gamma }_0 ,$ where $R_{x_0\to 1}$ denotes the achievable rate at $S{U}_1$ to decode x₀ and is given as:

$$R_{x_0\to 1}=lo{g}_2\left(1+\frac{{\lambda }_1{p}_0}{{\lambda }_1{\sum }_{l=1}^K{P}_l+1}\right)$$

(5)

Finally, the achievable rate at each k^th SU to decode $x_k$ can be expressed as [26]:

$$R_k=lo{g}_2\left(1+\frac{p_k{\left|g_k\right|}^2}{{\left|g_k\right|}^2{\sum }_{l=k+1}^K{p}_l+{\sigma }^2}\right)$$

$$R_k=lo{g}_2\left(1+\frac{{\lambda }_k{p}_k}{{\lambda }_k{\sum }_{l=k+1}^K{p}_l+1}\right)$$

(6)

Again, for the successful decoding of $x_k$ at each k^th SU, the above rate should satisfy

$$R_k\ge {\gamma }_k, k\in \mathsf{\Gamma }$$

(7)

As stated above, the proposed scheme guarantees the reliable transmission of primary signal using the MRC technique. Therefore, the achievable sum rate at the receiver Q can be obtained as [31]:

$$R_Q=lo{g}_2\left(1+\frac{P_{sel}{\left|h_{sel}\right|}^2}{{\sigma }^2}+\frac{{\lambda }_0{p}_0}{{\lambda }_0{\sum }_{k=1}^K{p}_k+1}\right)$$

(8)

In the above expression, the interference experienced from the PBS at Q is neglected in time slot 1 due to the absence of DL. For successful decoding of $x_0$ at Q, the above rate should satisfy $R_Q\ge {\gamma }_0$. Correspondingly, the minimum transmit power P_sel at SU_sel can be expressed as:

$$P_{sel}\ge \frac{{\sigma }^2}{{\left|h_{sel}\right|}^2}\left(2^{{\gamma }_0}-1-\frac{{\lambda }_0{p}_0}{{\lambda }_0{\sum }_{k=1}^K{p}_k+1}\right)$$

(9)

For a given transmit power P_S, the remaining power of the system should satisfy

$$P_{total}=P_0+P_{sel}$$

(10)

It is important to note that two time slot transmission processes can significantly reduce system transmit power while meeting QoS requirements, especially when the PBS and Q are separated by a large physical distance. Summing up the whole discussion, our optimization problem takes the following mathematical form:

$$\begin{gathered} \underset{p_0,p_1,\dots ,p_K}{\max }{\displaystyle \sum }_{k=1}^K{R}_k \\ \mathrm{such} \mathrm{that} \\ {C}_1: R_k\ge {\gamma }_{k, }k\in \mathsf{\Gamma } \\ {C}_2: R_{x_0\to 1}\ge {\gamma }_0 \\ {C}_3: p_0\ge p_1\ge \dots \ge p_K\ge 0 \\ {C}_4: {\displaystyle \sum }_{k=0}^K{p}_k=P_S \end{gathered}$$

(11)

Thus, our objective is to maximize the sum rate of all SUs under transmit power and QoS constraints. C₁ defines the rate threshold for successful decoding of $x_k$ at the k^th SU, C₂ defines the condition to ensure successful decoding of $x_0$ at each SU, and C₃ and C₄ define the individual transmit power and system transmit power constraint, respectively.

3. CI-Based Power Allocation Schemes

This section explains the CI-based power allocation schemes to solve the mathematical optimization problem in (11). First, the proposed EABC-based power allocation scheme is presented, followed by implementations based on PSO and GA, respectively.

3.1. Proposed EABC-Based Power Allocation Scheme

In order to understand the proposed enhanced version of ABC, first we revisit the optimization agents of the classic ABC algorithm, and then highlight the modifications proposed in the EABC algorithm.

Classic ABC stands among the most competent EA-based algorithms, offering a simple implementation with only two control parameters, i.e., maximum generation number (MGN) and limit. It consists of three colonies of honey bees (the search agents) known as Employed Bees (EBs), Onlooker Bees (OBs) and Scout Bees (SBs) [32]. EBs and OBs are the local search agents, whereas SBs act as global search agents to extend the search process to a larger search space. The search process of the ABC algorithm works as follows. First, EBs generate a neighborhood solution to each initialized solution and apply a greedy search process for updating. OBs act as followers and rely on the information shared by EBs to perform selective updates of the solutions based on their probability of fitness. Finally, SBs add strength to the potential solutions to prevent them from getting stuck in the local best, achieving this by randomly regenerating abandoned solutions. In the proposed EABC-based solution, two modifications are suggested as described below.

• OBs in the classic ABC algorithm perform selective updating of solutions by comparing the probability of fitness $\rho$ of each potential solution with a randomly generated number between 0 and 1. However, in EABC, we introduced a probability threshold δ to make an intelligent decision about selection of solutions by not updating any solution with a low fitness probability. This not only ensures the quality of each candidate solution but also saves the unnecessary hardware burden of updating weak solutions.
• SBs in the classic ABC algorithm randomly regenerate exhausted solutions. However, in EABC, the abandoned solutions are replaced with new ones that are randomly generated around the global best achieved so far to offer the regenerated solutions a good initial start.

The above two modifications of the classic ABC algorithm ensure that each potential solution in the population maintains a certain minimum performance threshold and enhances the quality of search process. The pseudocode for the proposed EABC-based power allocation scheme is provided in Algorithm 1.

Algorithm 1: Proposed EABC-based power allocation scheme

3.2. PSO-Based Power Allocation Scheme

PSO is a swarm-intelligence-based tool that operates intelligently by randomly spreading members of the swarm, commonly known as “particles,” in the search space of the problem [33]. It offers rapid, effective, and robust treatment of multiconstraint nonlinear optimization problems. PSO employs a velocity–position model in which position defines the search region and velocity defines the mutative direction to reach the global best in the search space. Both velocity $v$ and position $u$ are randomly initialized in the intervals $v_{min}\le v\le v_{max}$ and $u_{min}\le u\le u_{max}$, respectively. The information about velocity is then utilized to update the position. This process also involves sharing of individual and mutual experiences among the particles. After initialization, the velocity $v$ of each particle is updated in every generation using the following expression until the stopping criterion is met [34]:

$$v_{jk}^i=v_{jk}^{i-1}+{\alpha }_1{\beta }_1\left(c_{j\ast k}^{i-1}-u_{jk}^{i-1}\right)+{\alpha }_2{\beta }_2\left(b_{jk}^{i-1}-u_{jk}^{i-1}\right)$$

(12)

The corresponding position $u$ is updated using:

$$u_{jk}^i=u_{jk}^{i-1}+v_{jk}^i$$

(13)

The variables used in the above expressions are defined below.

${\alpha }_1,{\alpha }_2$: Cognitive coefficients for controlling the particle’s direction, usually set as ${\alpha }_1+{\alpha }_2\le 4$

${\beta }_1,{\beta }_2$: Uniform random variables generated in the interval [0, 1]

j*: Index of current best particle

$b_{jk}$ and $c_{j\ast k}$ denote the individual and collective experience of the particles respectively.

Using (12) and (13), each particle makes an effort to move towards the optimum by updating its position using the step function $v_{jk}$, which is added to the particle’s present position. This step may be positive or negative. The particle tries to achieve this objective using two search memories during each generation. One is the individual best $b_{jk}$ stored in its own history, and the other is the global best $c_{j\ast k}$ among all particles so far. However, it is very common that the algorithm falls into a local optimum while operating recursively, which results in reduced search efficiency and failure to achieve the global best [35]. To avoid this problem, several modifications and hybridization procedures to the classic PSO algorithm have been proposed in the literature to develop better control and balance between exploration and exploitation [36].

3.3. GA-Based Power Allocation Scheme

GA is recognized as a pioneering bio-inspired metaheuristic algorithm from the family of EAs. It follows an adaptive search procedure and is capable of handling multiobjective and multiconstraint numerical optimization problems with a noncomplex formation. GA explores the search space and stores a population of solutions or chromosomes in each generation. The chromosomes compete for resources and the winners produce more offspring, thus propagating their characteristics to the subsequent generations. For this purpose, a fitness value, related to the objective of the optimization problem, is the key criterion for ranking the individuals. A chromosome with a larger fitness value has high probability of resulting in an optimal solution to the problem [37,38].

After initializing a population of solutions, GA iteratively performs the operations of selection, crossover and mutation to update the population until the stopping criterion is met. The Algorithm 2 summarizes the sequence of steps involved in GA-based optimization.

Algorithm 2: GA-based Optimization

for i = 1:MGN 1. Tournament selection to choose the fittest individual 2. Crossovers to enrich the population with better chromosomes 3. Mutations to gain diversity and to avoid being trapped in local optima 4. Evaluate fitness function 5. Update local best solution end for Output: Global best with associated parameters

Although classic GA is competitive for handling complex and skewed data without prior assumptions, it is not efficient in finding solutions to problems that demand high accuracy [39]. Once GA approximately locates the optimized solution, it moves back and forth continuously to find the optimal solution, which significantly increases execution time and decreases search efficiency. Therefore, in order to increase optimization efficiency, GA has been hybridized with many other algorithms in literature, e.g., dynamic programming, neural networks, etc. [40].

4. Simulation Results and Discussion

In order to prove the effectiveness of the proposed EABC-based power allocation scheme, its performance is compared with the classic ABC algorithm and with the competent GA and PSO algorithms. The system parameters are set as follows. The number of PUs is set to 1, ${\gamma }_k=$ 1 bit/s/Hz, noise power is 10⁻⁸ mW, and path loss exponent is set to 2. The coordinates for the PBS are set to (0,0), whereas those for SR and Q are set to (50,−10) and (250,10), respectively, and thus the PBS and the receiver Q are separated far apart. For the SU cluster, the horizontal coordinates are randomly generated between 100 m and 150 m. In order to ensure a fair comparison among all CI-based algorithms, the transmit power allocated by the NOMA relay to each user is optimized according to (11). For PSO, ${\alpha }_1$ and ${\alpha }_2$ are set to 1.5 and $\left[v_{min},v_{max}\left]=\right[-9,+9\right]$. For all algorithms, population size is J = 20 and MGN = 500. The parameter settings for GA are provided in

Table 3. Parameter Settings for GA.

Parameters	Values
Selection	Stochastic uniform
Mutation	Adaptive feasible
Crossover	Heuristic
Crossover fraction	0.2
Function tolerance	$1\times {10}^{-15}$
Migration direction	Both ways
Scaling function	Rank

.

Figure 3 illustrates the convergence behavior of EABC as compared with classic ABC, PSO, and GA by observing the total transmit power of the system for a given $P_S=10 \mathrm{mW}, {\gamma }_0=$ 5 bit/s/Hz, δ = 0.8, K = 5. It can be seen clearly that EABC quickly converged to the global best in less than 15 generations, whereas ABC converged in approximately 25 generations. Both EABC and ABC converged quickly due to their simple implementation, involving fewer control parameters per generation, which in turn reduces the hardware burden.

Furthermore, EABC showed superior convergence performance to the classic ABC algorithm due to the high value of probability threshold δ set for fine-tuning of solutions, i.e., δ = 0.8. This smart behavior of updating the finest solutions not only improves the solution quality but also increases the speed of convergence. In contrast, PSO and GA converged in approximately 40 and 120 generations, respectively. The convergence performance of different global optimizers varies significantly depending upon the optimization parameters and the nature of the operations involved. In ABC and PSO, only the local and global best share fitness information with other candidate solutions. However, GA took the longest convergence time because the information is shared among all chromosomes in GA, and in addition, several operations and parameters are involved in every generation, which affects the settling time of the algorithm, thus requiring more generations to reach the global optima.

Figure 4 illustrates the sum rate of SUs varying the transmit power $P_S$ at the secondary NOMA relay. The required transmission rate of PU is set to ${\gamma }_0=$ 5 bit/s/Hz for reference. The results show that the sum rate of SUs increases as $P_S$ is relaxed; however, the required threshold for primary network is not met at low values of $P_S$, i.e., $P_S<20 \mathrm{mW}$. At the two extremes, the minimum transmit power required at the NOMA relay to satisfy the primary threshold is $P_S=20 \mathrm{mW}$ for EABC, while GA achieves the same rate at $P_S=32 \mathrm{mW}$. The performance of ABC and PSO lies in between the two, with 23 mW for ABC and 27 mW for PSO. Thus, EABC reduces power consumption by 13.95% compared to ABC, while 29.78% and 46.15% more power saving is achieved compared to PSO and GA, respectively. Once QoS of the primary network is met, the sum rate of SUs continues to increase with $P_S$. Moreover, we can clearly observe that EABC outsmarts all the three implementations for the whole range of $P_S$, keeping ${\gamma }_0$ fixed, followed by ABC in performance. PSO approaches ABC at several points, but classic GA significantly lags behind in performance to reach the global best. This is due to the weak exploitation capabilities of GA despite having the best exploration capabilities, due to which classic GA frequently gets stuck in the local optima. Thus, it can be concluded that the proposed EABC-based scheme offers the best performance while saving total transmit power.

Figure 5 shows the total power utilized by the proposed scheme, varying the transmit power of the secondary NOMA relay for ${\gamma }_0=$ 5 bit/s/Hz, δ = 0.8, and K = 5. Initially, for a low $P_S$ high remaining transmit power is required to meet the rate requirements of SUs. However, $P_{total}$ required by the system consistently and significantly decreases with an increase in $P_S$, since SR optimizes transmit power to accommodate all users while satisfying the constraints in (11), which in turn reduces the power required by the SUs to retransmit the PU’s signal. Finally, the EABC-based scheme demonstrates superior performance compared to other CI-based schemes, with a smooth transition as $P_S$ is relaxed.

In order to study the impact of varying the number of SUs on the transmit power of the system, Figure 6 plots $P_{total}$ against the number of available SUs, keeping $P_S=20 \mathrm{mW}, {\gamma }_0=$ 5 bit/s/Hz. As expected, $P_{total}$ decreases as the number of SUs increases. This is because a cognitive network having a significantly large number of candidate SUs increases the probability of selecting a relay having the best channel condition to the PU to retransmit the primary signal with low power. If we closely observe the transmit power behavior, it depicts a significant initial decrease as the number of SUs starts increasing, due to the added flexibility of the relay selection process. However, a minor improvement occurs in total transmit power as the number of SUs crosses 15, indicating that a potential set of 10 SUs available for selection is sufficient to obtain significant performance results.

Figure 7 illustrates $P_{total}$ required by the proposed scheme, varying $P_S$ for two cases, i.e., ${\gamma }_0=$ 4 bit/s/Hz and ${\gamma }_0=$ 5 bit/s/Hz. The NOMA relay optimizes the transmit power to accommodate the PU and each SU. It is observed that more power is required if the required transmission rate of the PU increases. Again, $P_{total}$ significantly decreases with an increase in $P_S$, since less power will be required by $S{U}_{sel}$ to successfully retransmit $x_0$. In addition, as compared to classic ABC, EABC offers more power-saving.

Finally, Figure 8 presents the sum rate achieved by EABC, varying the probability threshold δ. We have set δ = 0.3, 0.8 and 1 for EABC; however, classic ABC randomly generates δ, and picked δ = 0.4 for this simulation. The results of δ = 0.3 for EABC are almost overlapping with those obtained with classic ABC, due to the minimum difference in δ between the algorithms. However, significant difference is observed in performance as δ rises to 0.8, since it sets a high standard for OBs to pick up solutions for fine-tuning. Finally, δ = 1.0 updates the best solution, which validates the superior performance of the proposed EABC-based scheme.

5. Conclusions

In this article, a novel NOMA-based spectrum-sharing scheme is proposed for dual-hop CRNs in the worst-case scenario when direct communication between the primary transmitter-receiver pair is not possible due to deep shadowing. In this scenario, we mathematically formulated a sum-rate maximization problem under transmit power constraints to enable the primary communication via a NOMA-based secondary relay selected from a potential set of secondary users. The optimization problem is solved using the proposed enhanced-artificial-bee-colony (EABC)-based technique and compared using state-of-the art computational intelligence (CI) tools, i.e., classic ABC, GA and PSO, by varying different system parameters. Simulation results confirm the superiority of the EABC-based scheme over other CI-based techniques in terms of convergence time and transmit power saving. The proposed scheme is suitable even when the primary transmit-receive pair is separated by a long distance.