Multi-Objective Optimization of Joint Power and Admission Control in Cognitive Radio Networks Using Enhanced Swarm Intelligence

: The problem of joint power and admission control (JPAC) is a critical issue encountered in underlay cognitive radio networks (CRNs). Moving forward towards the realization of Fifth Generation (5G) and beyond, where optimization is envisioned to take place in multiple performance dimensions, it is crucially desirable to achieve high sum throughput with low power consumption. In this work, a multi-objective JPAC optimization problem that jointly maximizes the sum throughput and minimizes power consumption in underlay CRNs is formulated. An enhanced swarm intelligence algorithm has been developed by hybridizing two new enhanced Particle Swarm Optimization (PSO) variants, namely two-phase PSO (TPPSO) and diversity global position binary PSO (DGP-BPSO) variants employed to optimize the multi-objective JPAC problem. The performance of the enhanced swarm intelligence algorithm in terms of convergence speed and stability, while optimizing both the sum throughput and power consumption, is investigated under three different operational scenarios deﬁned by their single objective priorities, which translate to sum throughput and power consumption preferences. Simulation results have proven the effectiveness of the enhanced swarm intelligence algorithm in achieving high sum throughput and low power consumption under the three operational scenarios when the network includes an arbitrary number of primary and secondary users. Comparing the hybrid SPSO approach and the proposed approach, the proposed scheme has shown its effectiveness in increasing the sum throughput to 7%, 16%, and 31% under the multimedia, balanced and power saving operational scenarios, respectively. In addition, the proposed approach is more power efﬁcient as it can provide additional power savings of 3.58 W, 2.48 W, and 1.6741 W under the aforementioned operational scenarios, respectively.


Introduction
Recently, there has been a tremendous increase in the number of wireless devices such as smartphones, notepads and laptops. This makes spectrum scarcity the essential dilemma when launching new wireless services. Another fundamental issue that contributes negatively to the spectrum scarcity problem is the static spectrum allocation policy regulated by each and every national spectrum regulatory authority, such as the Federal Communications Commission (FCC) in the US, where a licensed user is assigned a fixed block of the spectrum on a long-term basis. This licensed user is typically known as a primary user (PU). The FCC conducted a study to figure out how the spectrum is being utilized and the results showed that the spectrum utilization varies temporally and geographically from 15% to 85% [1]. In [2], it is illustrated that only a small portion of the spectrum is heavily used, whereas the rest of the spectrum is either sparsely or moderately used. These findings of spectrum underutilization and inefficiency of use raise concerns about the static spectrum allocation strategy, which may no more be the choice for state-of-the-art wireless technologies. For instance, the so-called television white space (TVWS) concept is seen as a key enabler for radio regulators to invest in such a secondary spectrum market [3][4][5].
Cognitive radio (CR) technology is envisioned as a new paradigm that develops intelligence in wireless networks to resolve the spectrum scarcity problem. Conceptually, CR achieves better utilization of the available spectrum by allowing the primary users to share their spectrum with the secondary users. In general, the spectrum assignment policy in CR can be either overlay [6], underlay [7] or hybrid overlay/underlay [8]. In the overlay approach, the SUs are allowed to access the channels of PUs only when the PUs are not transmitting. This approach is practically challenging as it requires accurate and fast spectrum sensing. The underlay approach allows SUs to access the channels of PUs and transmit simultaneously with the PUs provided that the primary network is sufficiently protected. In underlay cognitive radio networks (CRNs), joint power and admission control (JPAC) is an attractive scheme that is proposed to realize the coexistence of PUs and SUs while both are allowed to share the same spectrum as long as no harmful interference is impacting the primary network. JPAC is a complex optimization problem that requires an efficient algorithm capable of jointly optimizing a given network's performance metrics. This research work focuses on addressing the JPAC problem in underlay CRNs. Motivated by its robustness and successful implementations for various engineering applications, new variants of the well-known particle swarm optimization (PSO) algorithm are developed and applied to jointly optimize the power consumption and the total sum throughput in an underlay CRN.
In underlay CRNs, the main concern is how to simultaneously control the transmit powers of PUs and SUs and select the eligible SUs who can be admitted to the network. It is a very complex operation to find the best channel assignment for SUs since there exists an extremely large number of possible solutions. This problem has been verified NP-hard [9][10][11]. In addition, finding the optimal power vector that jointly maximizes the total system throughput and minimizes power consumption is a very sophisticated task. In fact, there exists an intriguing relationship between system throughput and the amount of power consumption. Removing SUs aggressively leads to network underutilization even though a lower total power is consumed. On the other hand, the best network performance is achieved by admitting as many SUs as possible, but a higher total power is then consumed. As a result, an optimization algorithm is required to handle this tradeoff and balance between the abovementioned contradicting objectives. In the literature on addressing the JPAC problem in CRNs, several research works have considered multi-objective (i.e., multiple performance metrics) optimization in overlay CRNs [12][13][14]. However, the overlay approach of CRN is practically challenging due to the need for very fast processing and accurate spectrum sensing capabilities. In underlay CRNs, most of the research works have considered a single objective (i.e., a single performance metric) when optimizing the JPAC problem [15][16][17].
There has been some recent work on multi-objective optimization in CRNs [18][19][20] where different objectives such as spectral efficiency and network capacity are considered. Recently, the authors utilized genetic algorithms to develop a multi-objective optimization framework that aims to optimize spectral efficiency and transmission performance for spectrum allocations in the Internet of Things (IoT) CRNs [18]. The work in [19] applied reinforcement learning to address the problem of spectrum allocation in CRNs with the objective of optimizing spectrum efficiency and network capacity. Another recent work has considered optimizing power consumption, spectrum usage, and exposure in CRNs based on cloud architecture [20]. Considering energy harvesting cognitive radio sensor networks, the authors in [21] utilized dual decomposition to separate the NUM problem into sub-problems and then solving each sub-problem separately. According to the results, the proposed method achieves better performance when compared with the traditional approaches. Recently, the problem of NUM has been tackled in CR multichannel wireless networks by applying reinforcement learning techniques [22]. The proposed algorithms allow users to learn good spectrum access policies online. Although multi-objective optimization of the JPAC problem in underlay CRNs has been studied, applying enhanced swarm intelligence to jointly solve the power allocation and admission control in CRNs has not been well investigated yet.
Evolutionary algorithms, like PSO and genetic algorithm (GA) have been successfully applied to solve several real-world engineering problems, including CR problems [23][24][25]. In particular, PSO is arguably ranked top among the list of meta-heuristic approaches due to its simplicity, few controlling parameters, and satisfactory results at a very low computational time. Similar to meta-heuristic approaches, PSO does not provide perfect accuracy; however, it attempts to reach near-optimal solutions in a relatively short period. In several cases, it outperforms various evolutionary algorithms such as GA [26], [27] and ant colony optimization (ACO) [27]. As such, PSO and its hybridized variants have been used in various applications such as in smart agriculture [28], indoor and outdoor tracking [29], etc. However, PSO suffers from premature convergence [30]. In addition, the particles of PSO stagnate in the late phases of the searching process, which causes no further improvements.
These two major drawbacks of PSO occur as a result of no proper balance between exploration and exploitation. Exploration is defined as searching an extensive area in the space, while exploitation is focusing the search around a promising area. Therefore, it is essential to develop new enhanced PSO variants that can be efficiently applied to jointly optimize the problem of power and admission control in underlay CRNs.

Joint Power and Admission Control
There has been a significant effort with different objectives to address power and admission control in underlay CRNs. Several techniques, such as evolutionary and removal algorithms and game theory have been used to address this problem.
The authors in [31] compared the performance of four common removal algorithms, namely Single or Multiple Accumulative Removal Technique (SMART), Stepwise Maximum Interference Removal Algorithm (SMIRA), Stepwise Removal Algorithm (SRA) [32], and Power Reduction Removal Algorithm (PRRA-K(R)). The performance objective of these algorithms was to find the maximum number of SUs under QoS requirements. Among the four removal algorithms, SMART and SMIRA(R) are reported to be the best two removal algorithms. Ref. [33] SMART and SMIRA(R) algorithms, by adding interference constraint, results in two new removal algorithms, namely, I-SMART and I-SMIRA(R), which are less complex as compared to SMART and SMIRA(R). However, their results were suboptimal. Ref. [34] solved the problem of spectrum sharing by proposing a framework that jointly admits the existence of secondary links in the network and allocates power to each SU. To decide which secondary links are admitted based on QoS satisfaction, a removal algorithm called one-step is proposed. This algorithm is fast; however, it is very selfish. As a result, the authors developed another removal algorithm named one-by-one to overcome this problem. The aim was to find the maximum sum throughput that is achieved by both the primary users as well as the admitted secondary users. Nevertheless, it did not consider maximizing the number of allowed secondary users to admit in the network. Based on gradual removal techniques, ref. [16] developed a distributed algorithm that controls the power of secondary users in the network. This algorithm is known as a temporary removal and feasibility check (DFC). The concept of DFC is to temporarily remove a secondary user if its transmit power is higher than its maximum allowable power. However, a secondary user can re-transmit if its transmit power falls below a certain threshold. The proposed algorithm improved the power consumption in underlay CRNs. Nevertheless, power consumption can be reduced further. In addition, maximizing the system throughput was not considered.
In [35], a framework based on game theory for solving the channel allocation problem for two distinct cases; cooperative and non-cooperative, was presented. In both cases, the SUs can cause harmful interference to the primary users. In [36], game theory is applied to develop a noncomplex fully distributed power control algorithm. The objective was to enhance the performance of the CR network by maximizing the data rate of SUs. However, the achieved results are sup-optimal. In addition, controlling the power of the PU was not considered. In [37], the power of each SU is controlled via pricing. The primary user charges each secondary user per interference power. The communication that occurs between PU and SUs is modeled as a Stackelberg game where the PU and SUs act as the leader and followers, respectively. The main objective was to find the best price for the primary user in order to maximize its revenue. The proposed pricing technique proved that it performs better than the non-uniform pricing technique presented by [38] in finding the optimal price. However, minimizing the total power consumption of PUs and SUs was not considered.
The authors in [15] applied several binary PSO (BPSO) variants in order to solve the channel allocation problem and their main objective was to maximize the sum throughput achieved by both PUs and SUs in an underlay spectrum network. The BPSO showed good performance in terms of maximizing the sum throughput. However, the authors assumed that the transmit power of PUs and SUs are the same, which results in non-optimality. In addition, a distributed approach is used, which is impractical for swarm algorithms since such algorithms require a central node to be placed. Based on GA, ref. [39] proposed a power allocation algorithm in underlay CRNs. The work considered the case when there is only one PU exists in the network. The objective of the work was to either maximize the system capacity or to minimize the total power consumption. Optimizing the system capacity and total power consumption jointly was not considered. Ref. [40] developed an improved artificial fish swarm algorithm (IAFSA) in order to control the power of SUs so that the interference at the PU is minimized. Moreover, the algorithm is used to minimize the total power of SUs. The performance of IAFSA was compared with those of other evolutionary algorithms such as PSO and chaos PSO. Although the performance of IAFSA is better than two of the weakest PSO variants (standard PSO and chaos PSO), IAFSA was not compared with other powerful PSO variants. Furthermore, the presented system model is not practical since swarm algorithms must be placed at a central node. In addition, the authors did not consider several issues, such as minimizing the power of PUs and maximizing the total throughput jointly.
Besides removal algorithms, game theory and evolutionary algorithms, there are other techniques such as auction, and bisection searching method that have been proposed to address the JPAC problem. In [41], two different auction strategies for spectrum sharing are studied. The first auction strategy charges SUs a price for the received SINR. In the second auction strategy, SUs pay for their transmit powers. The power auction performs better than the received SINR auction in terms of revenue collection. However, they have similar performance when the number of users increases. The authors of this work did not take into consideration the QoS of SUs. Ref. [42] proposed a centralized low-complex algorithm to address the JPAC problem in CRNs. Bisection searching method is used to maximize the number of SUs who can peacefully coexist with the PUs. Although the proposed algorithm is less complex as compared to other existing algorithms, such as the optimal searching algorithms [43] and the sequential searching algorithms [44], it only achieves sub-optimal solutions. Ref. [45] addressed the problem of controlling the access of SUs in CRNs while the primary network is protected via pricing. The concern was to minimize the power consumption by both PUs and SUs as well as to find the maximum number of SUs who can coexist peacefully with the PUs. Although the proposed pricing technique reduced power consumption, the obtained results are not optimal. In addition, maximizing the total system throughput was not considered.
In [46], two centralized algorithms, namely the Effective Stepwise SU Removal with Primary users' protection Algorithm (ESRPA) and the Effective Link Gain ratio Removal Algorithm (ELGRA), are proposed to solve the problem of JPAC in underlay cellular CRNs based on SINR constraints. It was shown that ESRPA outperforms ELGRA in performance, while the latter is better in terms of complexity. However, the optimality of the achievable performance is not investigated. Instead of an underlay CRN scenario, an energy-efficient scheduling and power control algorithm is proposed in interweaving CRNs [47]. The authors in [48] proposed a quality of experience (QoE) oriented rate control and resource allocation for cognitive machine-to-machine (M2M) communication in spectrum-sharing OFDM networks, but the power allocation was not taken into account. In addition, the literature reveals that the JPAC problem has been studied in various non-CR network models, channel access strategies and applications including heterogeneous networks (HetNets) [49][50][51], non-orthogonal multiple access (NOMA) [52][53][54] R47,48,49, orthogonal frequency division multiple access (OFDMA) [55][56][57], D2D/M2M communication [58][59][60] and beamforming [49,61,62].
Obviously, the JPAC problem in CRNs has been studied by many researchers, as discussed above. However, most of these research works are limited to single performance objectives, suffer from high complexity, consider different spectrum access strategy/network model with no CR involved or do not provide optimal solutions. Unlike the state-of-the-art work, the proposed work develops a novel hybridized PSO approach that can efficiently address the problem of joint power allocation and admission control. A continuous PSO is developed to perform power allocation, while an enhanced binary PSO is proposed to select eligible users that can utilize the available spectrum without causing harmful interference to primary users. The effectiveness of the proposed two novel PSO variants, and their operations in concurrently and jointly optimizing the performance of the CRN network, is verified. The enhanced performance of the CRN network with the proposed continuous and binary PSO variants justifies the feasibility of this hybrid approach in optimizing the combined continuous and binary nature of the JPAC optimization problem.

Particle Swarm Optimization
PSO consists of a number of particles called a swarm where each particle can fly in the search space in order to find a better position. Each particle has a velocity and position vectors as follows: where V i is the velocity vector, X i is the position vector, D is the number of dimensions, and N is the population size. The initial positions of the particles are randomly created. Then, in each iteration, particles follow a leader known in PSO as the global best position (gbest), which is the best position that has been found so far in the whole swarm. Moreover, particles follow their own historical best position, Pbest. Each particle updates its velocity and position based on the following equations: where w is the inertia weight, c 1 and c 2 are the cognitive and social acceleration coefficients. rand 1 and rand 2 are two uniform random values generated within [0,1]. v id has a specific range set by |v id | < v max . Kennedy and Eberhart introduced PSO in a binary representation [63]. The binary PSO (BPSO) is used to solve binary problems, where a decision will be "yes" or "no"; true or false. Similar to the continuous PSO, BPSO updates its velocity based on Equation (3).
Then, the velocity update equation is limited to the range [0,1] using the sigmoidal function, which is defined as follows [64]: Particles in BPSO update their positions as follows: where r 3 is a uniformly distributed random value in the interval [0,1]. Unlike the case of continuous PSO, which was extensively researched, there has been a limited number of research works that attempted to modify the original BPSO to improve its performance. In [65], an essential binary particle swarm optimization (EPSO) was introduced where the velocity component of PSO was omitted. The original BPSO was also modified in [66] by using the genotype-phenotype concept resulting in a new BPSO variant commonly referred to as the modified MPSO (MPSO). In this approach, each particle updates its velocity and position based on the genotype-phenotype particle. In addition, the genotype particle is iteratively mutated, which allows for better exploration of the search space.

System Model
In this work, the proposed system model (shown in Figure 1) includes N secondary links and M primary links (primary channels) sharing the same spectrum band with higher priority for PU access. It is assumed that all primary and secondary links are active due to the transmission of PU and SU transmitters, respectively. A unique channel is assigned to each primary link, while any primary channel can be allocated for several secondary links. In Figure 1, the numbers that appear beside the links denote the link numbers, while the numbers in braces and brackets denote the primary channels assigned to the primary and secondary links, respectively. Each primary or secondary receiver, whose link uses the same channel with active transmitters, is influenced by some amount of interference. The measurement of this interference is evaluated by the signal to interference noise ratio (SINR) expressed in dB. The mathematical formula for the j th secondary receiver is as follows [67]: where P is the transmitted power, n is the attenuation factor, noise j is an additive white Gaussian noise (AWGN) at the j th secondary receiver, lds(j) is the distance between the transmitter and receiver of the j th secondary link, dss(l, j) is the distance from the l th secondary transmitter to the j th secondary receiver, dps(l, j) is the distance from the i th primary transmitter to the j th secondary receiver, where Φ is the full set of SUs who use the same primary channel. Similarly, the SINR at the i th primary receiver is given by: where ldp(i) is the distance between the transmitter and receiver of the i th primary link, dps(l, j) is the distance from the l th secondary transmitter to the i th primary receiver.

Formulation of JPAC Multi-objective Optimization Problem
The performance objective of maximizing the system capacity achieved by both PUs and SUs is first considered. The channel capacity of the primary link i (capacity i ) and secondary link j (capacity j ) are expressed as follows: where B is the bandwidth of the primary channel. The total system throughput achieved by PUs and SUs is expressed as follows: where x j is either zero or one, x j = 1 indicates that a secondary link is selected whereas x j = 0 indicates that a secondary link is not selected. SINR represents the minimum signal power level that must be achieved in order to transmit properly. The higher the SINR, the better the Quality of Service (QoS). For instance, the value of SINR must be at least 3 dB for good voice transmission [68]. SI NR pl and SI NR sl denote the minimum SINR that must be achieved by a PL and an SL, respectively. Since PUs have higher priority than SUs, SI NR pl is set to be greater than SI NR sl . Thus, the primary network can then gain higher protection against interference.
The second performance objective is to minimize the total power consumed by PUs and SUs. This objective can be mathematically formulated by the following optimization problem: In the JPAC problem, the transmit power of PUs and SUs as well as the links admission in the underlay CRN has to be controlled. To enhance the overall performance of the underlay CRN, it is essential to simultaneously maximize the system throughput and minimize power consumption. The JPAC problem can be formulated as a multi-objective optimization problem that aggregates the two individual objectives; maximizing the total sum throughput and minimizing the power consumption. To do so, the objective functions f 1 and f 2 must be first normalized as follows: where f 1max and f 2max are the maximum values of f 1 and f 2 , respectively. To find f 1max , an exhaustive research is carried out. f 2max is found by calculating the maximum allowable power that PUs and admitted SUs can consume. The well-known weighted sum approach is then used, and the two objectives can be combined into a multi-objective function as follows: where ω 1 and ω 2 are weighting coefficients having values in the range of [0,1], and they indicate the relative significance of the two objective functions. A higher value of ω 1 indicates that the first objective is more important than the second objective and vice versa. It should be noted that the weighting coefficients must satisfy the constraint ω 1 + ω 2 = 1.
The main objective is formulated as follows:

Enhanced Swarm Intelligence for JPAC Problem Optimization
The problem of multi-objective JPAC is solved using an enhanced swarm intelligence that hybridizes the continuous PSO (i.e., SPSO) and the binary diversity global position binary PSO (i.e., DGP-BPSO). For simplicity, the continuous and binary PSO variants are denoted as CPSO and BPSO, respectively. In general, the BPSO is used to identify whether an SU is selected or not whereas the CPSO is used to allocate transmit power levels for PUs and SUs. The subscripts c and b are used to distinguish between the variables, abbreviations and parameters of the CPSO and BPSO, respectively. For example, in CPSO, gbest is replaced by gbest c , which represents the best particle in the whole swarm that stores the best power allocation for both SUs and PUs. Similarly, In BPSO, gbest is replaced by gbest b , which represents the best channel assignment. Algorithms 1 and 2 illustrate the steps of how the DGP-BPSO and TPPSO, respectively, of the enhanced swarm intelligence are applied to solve the JPAC problem in the proposed underlay CRN model. The CPSO is used for power control, whereas the BPSO is used for admission control. CPSO and BPSO are concatenated to form the enhanced swarm intelligence used to solve the entire JPAC problem. For j = 1 : SL S STEP 33: If K(j) = 0 STEP 34: gbest b (j) = 0 STEP 35: Elseif K(j) = gbest b (j) STEP 36: The binary swarm consists of S b particles and the dimension of each particle is the number of secondary links (SLs). The BPSO vectors are described as follows: where v bmax is the maximum binary velocity. • Every particle member x idb of the particle vector X ib is either Zero or one (one indicates that an SL is selected, while zero indicate that a SL is not selected). • Every best position member P idb is either zero or one.
Following the work in [9], two new matrices (X ib , Pbest ib ) of dimension S b × N are created, where S b is the population size and N is the total number of the secondary links. X ib and Pbest ib are used to store the primary channels that have been assigned to the secondary links. Moreover, a Spectrum Status Vector (SSV) is created, where the indices of the vector represent the number of the primary channel, while an element of the vector represents the number of the primary link that uses the primary channel. It should be noted that for each x idb there is an x idb . The state of x idb is determined as follows: Furthermore, for each Pbest idb there is a Pbest idb which keeps the best channel assignment. The definitions of SSV and X ib and X ib are illustrated in Figure 2. As shown in Figure 2, it is clear that SLs 1, 3, 4 are admitted; thus, X ib randomly assigns channels to the admitted SLs from a set of 5 primary channels (PCs) in SSV. SSV and X ib determines the possible assignments for PLs and SLs. For instance, SL 1 is allowed to share PC 3, looking into the SSV it is seen that channel 3 is occupied by PL 5; therefore, SL 1 can share PC 3 under QoS requirements. Figure 2. Illustration of the spectrum status vector and X ib , X ib [15]. Algorithm 2 Pseudo-code for the power control with two-phase PSO (TPPSO) STEP 1: Receive X ib , X ib , and SSV from the DGP-BPSO and Initialize the swarm size S c STEP 2: Set the range for the power of SL and PL to be P max = 1 and P min = 0 STEP 3: Generate the power vector X c STEP 4: Set V c ← 0 , Pbest c ← X c STEP 5: Repeat STEP 6: For K = 1 : S c STEP 7: Calculate SINR at SL and PL using X c , SSV, and Y STEP 8: Calculate SINR at SL and PL using Pbest c , SSV, and Y STEP 9: Calculate fitness using Equation (16)  The continuous swarm consists of S c particles and the dimension of each particle is the number of SLs and the number of PLs. The continuous PSO vectors are described as follows: • Every member v idc of the velocity vector V ic is in the range [−v cmax , v cmax ] where v cmax is the maximum continuous velocity. • Every particle member x idc of the particle vector X ic and every best position member P idc are restricted to have values in the range [P max , P min ] where P max and P min are the maximum and minimum allowable transmit power.
In continuous PSO, each particle represents the allocated transmit powers for PUs and SUs. The first part of the particle is to allocate the power for PUs and the rest of the particle is to allocate the power for SUs. In case an SL is not selected, then its transmitted power is set to 0. An example of a continuous PSO swarm is shown in Table 1. In this example, there are 2 PUs and 4 SUs. Therefore, the first two dimensions of the particle is the power allocation for PUs, while the last 4 dimensions are the power allocation for SUs. In the first particle, the first and second PUs are allocated transmitted power of 0.010 and 0.050 W, whereas the allocated transmit power of the first, second, third, and fourth SUs are 0.900, 0.003, 0, and 0.910 W, respectively. The first particle indicates that the first, second, and fourth SLs are part of the solution, whereas the third SL is not selected. Thus, its transmit power is set to 0. Figure 3 shows an example of a candidate solution that consists of binary and continuous particles.  It is noteworthy that not all candidate solutions are valid. In other words, some candidate solutions are able to achieve the QoS requirements (valid solution) while some candidate solutions are not (invalid solution).

Experimental Results and Discussion
The main aim is to optimize the objective function in Equation (16) using the proposed enhanced swarm intelligence. In Figures 2 and 4, it has been explained how the continuous PSO (TPPSO) and the binary PSO (DGP-BPSO) of the proposed enhanced swarm intelligence are used to optimize the power control and admission control, respectively. Three different operational scenarios are considered, as shown in Table 2. The performance of enhanced swarm intelligence of TPPSO and DGP-BPSO is compared with hybrid combinations of the continuous PSO variants listed in Table 3 and the binary PSO variants listed in Table 4 in terms of solution accuracy, convergence speed and stability. The multimedia scenario is suitable for cases when the total throughput is of extreme importance, whereas the power consumption is relatively less important. The balanced scenario is for cases when the total throughput and power consumption are equally important. The power-saving scenario is the opposite case of the multimedia scenario. The assigned weights for the multimedia and power-saving modes are arbitrary and meant to overweight a specific objective as compared to the other.  The parameter settings of the continuous and binary PSO variants are listed in Tables 3 and 4, respectively. Similar to the works published in [69][70][71], results are averaged over 30 runs in order to achieve better accuracy.
A simulation model, where all the secondary and primary links are deployed in an area of 5 km × 5 km is considered. The maximum distance of a PL or an SL is limited to 1000 m. The numbers of PLs and SLs are chosen to be 5 and 10, respectively. The noise is assumed to be an AWGN of 5 × 10 −15 W. Table 5 summarizes the CR simulation parameters. The enhanced swarm intelligence of TPPSO and DGP-BPSO is compared with hybrid combinations of the continuous and binary PSO variants listed in Tables 3 and 4, respectively, in terms of solution quality, convergence speed and reliability. The results obtained from one run are not reliable since the PSO process is random. Therefore, the results are averaged over 30 runs. In this experiment, as seen in Tables 6-8, there are a  total of 30 hybrid PSO combinations since there are six continuous PSO variants and five  binary PSO variants. Tables 6-8 show the results of all the hybrid PSO variants for the multimedia scenario, the balanced scenario and the power saving scenario, respectively. For each hybrid combination (e.g., TPPSO and BPSO), the average fitness, average data rate, average power, SD, and the average number of admitted SUs are recorded.

Multimedia Scenario
Under this scenario, Table 6 records the average results of all the hybrid PSO combinations when the sum throughput is more important than power consumption. Figure 4 shows the convergence speed of the hybrid PSO combinations under this scenario.
As shown in Table 6, it is clear that the SPSO with DGP-BPSO achieves better average fitness as compared with the other SPSO hybrids. Since the average fitness in this scenario is highly influenced by the achievable average sum throughput, SPSO with DGP-BPSO outperformed the other SPSO hybrids in terms of average fitness because it achieved higher average sum throughput. It is noteworthy that the average fitness increases from 70% (the worst average sum throughput case achieved by SPSO with GA) to 76% (the best average sum throughput case achieved by SPSO with DGP-BPSO). The SPSO with DGP-BPSO obtains the highest average admitted SUs (i.e., 7.53). This indicates that there is a removal of SUs with an average of 2.47. The main reason for the removal of SUs is that not all SUs are able to satisfy the SINR requirement. Figure 4a depicts the convergence speed of the hybrid SPSO variants. As shown in this Figure, the SPSO with DGP-BPSO, SBPSO, EPSO, MPSO, and GA, reach their corresponding average fitness shown in Table 6 at iteration number 370, 252, 452, 279 and 289, respectively. Although the SPSO with SBPSO is the fastest hybrid variant to converge to the average fitness, the SPSO with DGP-BPSO managed to reach the same average fitness achieved by the SPSO with SBPSO (i.e., 0.73) at iteration number 44. The SPSO with DGP-BPSO required 326 iterations to increase the average fitness from 0.73 to 0.77. The performance of SPSO in terms of reliability is satisfactory since it has a small SD.
PSO-LVIW, with its binary combinations, performs slightly better in finding the maximum average fitness compared with the SPSO, particularly when PSO-LIVW is hybridized with DGP-BPSO.
As seen from Table 6, HPSO-TVAC improves the average fitness by achieving higher sum throughput except for the HPSO-TVAC with DGB-PSO. HPSO-TVAC with DGP-BPSO achieves an average fitness of 0.80, which is exactly the same average fitness achieved by PSO-LVIW with DGP-BPSO. The reason that HPSO-TVAC with DGP-BPSO and PSO-LVIW with DGP-BPSO achieve the same average fitness through PSO-LVIW with DGP-BPSO obtained higher average sum throughput is that HPSO-TVAC with DGP-BPSO controls the power more efficiently, which helps to increase the average fitness. HPSO-TVAC does not only improve the average fitness, it also improves power consumption. GPS's performance is quite similar to HPSO-TVAC in terms of average fitness, average sum throughput, and average power. Among all GPS hybrids, GPS with DGP-BPSO scored the highest average fitness by achieving high average sum throughput and low average power consumption. Although CAPSO outperformed SPSO and PSO-LVIW to maximize the average fitness, CAPSO does not perform better than HPSO-PSO or GPS.    Table 6 shows that TPPSO performs well in maximizing the average fitness, especially when it is hybridized with DGP-BPSO (refer to Var. No. 26 in Table 6) and MPSO (refer to Var. No. 29 in Table 6). TPPSO with DGP-BPSO increases the average fitness from 73% to 79%, as compared with the SPSO with SBPSO. Besides the great capability of TPPSO to increase the sum throughput, TPPSO shows good performance in controlling the power efficiently. In Figure 4f, the convergence speed of the hybrid TPPSO is shown. The TPPSO with its five binary PSO variants converge to their average fitness values shown in Table 6 at iteration number 234, 219, 433, 315, and 217, respectively. The hybrid TPPSO with DGP-BPSO reaches an average fitness of 0.80 at iteration 38 and spends 196 more iterations to increase the average fitness from 0.80 to 0.83. Similar to the other PSO variants, TPPSO showed it is a stable variant too.
Overall, SPSO and PSO-LVIW has shown satisfactory performance in maximizing the average fitness. However, their performance in controlling the power is relatively low. Both HPSO-TVAC and GPS achieves better average fitness results and controls the power more efficiently as compared with the SPSO and PSO-LVIW. CAPSO performs slightly better as compared with SPSO and PSO-LVIW but not better than HPSO-TVAC and GPS. TPPSO shows great performance in finding the maximum average fitness. Among all 30 hybrids, TPPSO with DGP-BPSO achieves the highest average fitness. TPPSO also proves that it is the best variant that controls power efficiently. In addition, TPPSO outperforms all other compared PSO variants in terms of convergence speed. For instance, as Figure 4a, 4e and 4f show, the number of iterations required to reach average fitness achieved by SPSO with DGP-BPSO, CAPSO with DGP-BPSO, and TPPSO with DGP-BPSO are 400, 350, and 90, respectively. This demonstrates that TPPSO has a fast convergence speed as it does not require many iterations to reach average fitness, unlike other PSO variants.

Balanced Scenario
This scenario considers the case when the sum throughput and the power consumption are equally important. Table 7 shows the result that is obtained by all the PSO hybrids for this scenario.
From Table 7, it is obvious that the SPSO performs better in terms of average fitness when it is combined with MPSO. The average fitness achieved by the SPSO and DGP-BPSO is very close to the average fitness achieved by the SPSO and MPSO. The performance of the SPSO decreases when it is combined with GA. Overall, the best performance of the SPSO in terms of average fitness is achieved when it is combined with MPSO, followed by DGP-BPSO, EPSO, SBPSO, and GA. Figure 5 shows the convergence speed of all hybrids for the balanced scenario. The convergence speed of the hybrid SPSO variants are shown in Figure 5a. It is observed that both the SPSO with DGP-BPSO and SPSO with DGP-BPSO outperform the other hybrid variants, in terms of convergence speed. The SPSO hybrids obtained a small SD value, which indicates their stability. The PSO-LVIW achieves similar average fitness results as the SPSO. The best performance in terms of average fitness is obtained by the PSO-LVIW with DG-BPSO and PSO-LVIW with EPSO. Although PSO-LVIW with EPSO and PSO-LVIW with DG-BPSO achieve the same average fitness, PSO-LVIW with DG-BPSO is more stable than PSO-LVIW with EPSO. Table 7 shows that PSO-LVIW with SBPSO, EPSO, and GA obtains better average fitness results as compared to SPSO with SBPSO, EPSO, and GA. All the hybrids of PSO-LVIW are shown to be stable, particularly the PSO-LVIW with MPSO, as it achieves the smallest SD. Table 7 shows that HPSO-TVAC performs well in optimizing the fitness, specifically when it is combined with DGP-BPSO. Comparing SPSO with DGP-BPSO and HPSO-TVAC with DGP-BPSO in terms of average fitness, HPSO-TVAC with DGP-BPSO increases the average fitness from 76% to 88%. In addition, HPSO-TVAC with DGP-BPSO provides additional average power savings of 2.15−0.29

2.15
× 100% = 86.5%. It is also noted that HPSO-TVAC with DGP-BPSO has the ability to admit more SUs, which caused the sum throughput to increase. On the contrary, HPSO-TVAC with GA supports fewer SUs, which caused the sum throughput to decrease. A higher number of admitted SUs does not always indicate a higher sum throughput. For example, HPSO-TVAC with SBPSO supports average admitted SUs of 6.53 and achieves a sum throughput of 2123.9 Mbps, whereas HPSO-TVAC with EPSO supports slightly less SUs (average of 6.46), but with higher sum throughput (2204.7 Mbps). The reason for this is because the supported 6.46 achieved higher SINR (the higher the SINR, the higher the sum throughput, as seen in Equation (9). The HPSO-TVAC with its all hybrids, shows their reliability by achieving a small SD.
The performance of GPS and its all combinations in maximizing the fitness is close to the performance of HPSO-TVAC. GPS also shows that it is a stable PSO variant. Although CAPSO with DGP-BPSO performs better than other hybrids of CAPSO in terms of average fitness, its performance is not better than HPSO-TVAC with DGP-BPSO nor GPS with DGP-BPSO. CAPSO does not perform well in finding the optimal power, which caused the average fitness to decrease. Table 7 shows that TPPSO achieves high average fitness by balancing between maximizing the sum throughput and power consumption. TPPSO with DGP outperforms all other hybrids in terms of the achievable average sum throughput and the consumed power. Figure 5f depicts the convergence behavior of all the hybrid TPPSO variants. It is clear that TPPSO with DGP-BPSO converges faster than the other hybrid TPPSO variants.

Power Savings Scenario
This scenario considers the case when power consumption is more important than sum throughput. The results for this scenario for all the PSO hybrids are shown in Table 8. The convergence speed for all the hybrid PSO variants under the power saving scenario is shown in Figure 6.  Table 8 shows that the SPSO achieves higher average fitness as compared to the SPSO in Table 6 (Multimedia scenario). In this scenario, the SPSO manages to control the power more efficiently, at the expense of average sum throughput, as compared to the multimedia scenario. The reason that the SPSO consumes less average power is because it supports fewer SUs. The fewer the admitted SUs, the lower the power consumption, and the lower the power consumption, the higher the average fitness. The performance of PSO-LVIW, in terms of optimizing the average fitness in this scenario is similar to the performance of SPSO. HPSO-TVAC improves average fitness by simultaneously achieving high sum throughput and low power consumption. The best and worst performance of HPSO-TVAC is achieved when HPSO-TVAC is hybridized with DGP-BPSO and GA, respectively. HPSO-TVAC with DGP-BPSO increases the average fitness from 78% to 93% and saves additional power of (1. 68 Figure 6f illustrates the convergence speed of all the hybrid TPPSO variants. It is observed that all the hybrid TPPSO variants converge fast.
In this scenario, SPSO and PSO-LVIW consumed less power as compared with Scenario 1 because they support less number of SUs. HPSO-TVAC and GPS control the power more efficiently as compared with SPSO and PSO-LVIW without the need to remove a large number of SUs. CAPSO performs better in terms of minimizing the average power when it is compared with SPSO and PSO-LVIW. However, this is not true when CAPSO is compared with HPSO-TVAC and GPS. Among all the hybrid variants, TPPSO particularly when it is hybridized with DGP-BPSO shows the best performance in terms of optimizing the average fitness, sum throughput, power, and admitted number of SUs.

Performance Summary under Various Scenarios
As extracted from Tables 6-8, the proposed swarm intelligence's performance with its hybridized variants of TPPSO and DGP-BPSO under various operational scenarios is presented in Table 9. In the previous section, it has been shown that the proposed TPPSO and DGP-BPSO generally outperform all other hybrids in terms of the achievable fitness, convergence speed, and stability, as well as in terms of the average sum throughput, power consumption and SU admission. As shown in Table 9, the performance of the proposed TPPSO with DGP-BPSO under the three operational scenarios is justifiable. Under the multimedia mode, where maximizing the throughput is prioritized, the average sum throughput is higher than that under the power saving mode. On the other hand, under the power saving mode, where minimizing the power consumption is favoured, the average power is lower than that under the multimedia mode. It is noteworthy to state that the performance of the proposed swarm intelligence algorithm of TPPSO with DGP-BPSO under the balanced mode is justifiable, with an average fitness of 0.90 over the 30 runs. Under this balanced scenario, the achievable average sum throughput is slightly higher than that of the multimedia scenario, while the average power of 0.01 is within those of the other two scenarios. The average admitted SUs is higher than those of the multimedia and power saving modes with a stable performance presented by its low standard deviation of ±5%. Due to the promising performance of the proposed swarm intelligence algorithm under the balanced scenario, the later can be assumed to be the default operational scenario of the system.

Conclusions
A critical challenge in underlay CRNs is how to control the power of PUs and SUs and how to control the coexistence of SUs with PUs under QoS and interference constraints. Several works have attempted to address the aforementioned research questions. Nevertheless, the main focus was either to maximize the sum throughput or to minimize the power consumption. However, for higher spectral and power efficiency of underlay CRNs, it is essential to jointly maximize the sum throughput and minimize the power consumption.
In this work, a multi-objective function that aims at jointly maximizing the sum throughput and power consumption in underlay CRNs is formulated. To solve the JPAC problem, two new enhanced PSO variants, namely two-phase PSO (TPPSO) and diversity global position binary PSO (DGP-BPSO) have been hybridized to form an enhanced swarm intelligence algorithm.
In the proposed underlay CRN, DGP-BPSO has been used to either admit or rejects SUs, whereas TPPSO is used as a power control algorithm. The performance of the enhanced swarm intelligence algorithm that hybridizes TPPSO and DGP-BPSO is verified by comparing it with several hybrid continuous-binary PSO combinations in terms of the achievable fitness of the multi-objective function, convergence speed, and reliability.
Based on the simulation results, it has been proved that the enhanced swarm intelligence realized by the hybrid combination of TPPSO and DGP-BPSO has outperformed all other hybrid PSO combinations in terms of jointly optimizing the sum throughput and power consumption, convergence speed, and reliability under the three proposed operational scenarios. As compared with the hybrid SPSO, the enhanced swarm intelligence has the ability to increase the sum throughput to 7% (multimedia), 16% (balanced), and 31% (power saving) operational scenarios, respectively. Moreover, the enhanced swarm intelligence has achieved additional power savings of 3.58 W, 2.48 W, and 1.6741 W under the aforementioned operational scenarios, respectively. As future work, the developed swarm intelligent approach can be implemented in heterogeneous networks to jointly maximized the overall throughput and minimize power consumption. Moreover, it can be utilized to jointly optimize the performance of power allocation and user association in massive MIMO networks. The flexibility of the swarm approach allows its implementations in a wide range of industrial applications, such as scenarios where minimal power consumption is crucial.

Data Availability Statement:
The data presented in this study are available on request from the corresponding author. The data are not publicly available since it is generated based on mathematical equations and programming source codes generated from MATLAB.

Conflicts of Interest:
The authors declare no conflict of interest.