Improved spectrum allocation scheme for TV white space networks using a hybrid of firefly, genetic, and ant colony optimization algorithms

Abstract

This study proposes a novel hybrid Firefly Algorithm, Genetic Algorithm, and Ant Colony Optimization Algorithm (FAGAACO) for spectrum allocation in TV White Space (TVWS) networks. The Genetic Algorithm (GA) was used in the design to provide cross-over chromosomes to both the Firefly Algorithm (FA) and the Ant Colony Optimization Algorithm (ACO), thereby improving the exploration abilities of FA and ACO and preventing FA and ACO from becoming trapped in local optimum. The proposed algorithm was implemented using MATLAB R2018a. Simulation results show that in comparison with a hybrid of the Firefly Algorithm and Genetic Algorithm (FAGA), the proposed algorithm achieved 13.03% higher throughput, 1.3% improved objective function value and 5.03% higher runtime due to the good accuracy of the proposed algorithm. Based on these improvements, the proposed algorithm is therefore an efficient spectrum allocation technique in TVWS networks.

1. Introduction

The existing wireless networks are distinguished by a static spectrum allocation policy where regulatory authorities allocate wireless spectrum to primary users (PUs) who are long-term license holders in various countries and territories. Due to increased demand for the spectrum, this policy is facing serious challenges as the spectrum is a scarce resource and expensive to acquire. However, the already licensed spectrum for example those that are assigned to TV broadcasters are well underutilized [1] which happens especially in less populated areas. There is thus a need for a dynamic spectrum sharing technique where the same licensed frequency band can be re-used by a secondary user to provide broadband communication services in remote areas provided there will be no interference to the primary user [2].

Television white space (TVWS) does not require a direct line of sight and can propagate up to four times as far as Wi-Fi at similar power [3]. These advantages make it a desirable target for cognitive radio-based spectrum sharing because of these propagation properties. This is quite a necessity, especially for developing countries where there is a high population of under-served. The regulatory bodies have formulated regulations that will allow Internet Service Providers (ISPs) to provide internet services using TVWS and are expected to come into effect from 2023 according to ITU [4]. The regulatory bodies in the United States, Europe, and Kenya have already developed formalities to allow the sharing of the TV band without causing interference to the existing networks. For this purpose, the cognitive radio network (CRN) and the system to which it operates need to scan the surrounding environment for electromagnetic waves. In this paper, we combine the two techniques of gaining awareness of electromagnetic waves i.e. access to a geographically-reference database containing spectral occupancy and spectrum sensing techniques [4]. The transition from analog TV to Digital Terrestrial Television (DTT) reduced the available spectrum for TV transmission, with some auctioned off and the rest assigned to DTT. In the most recent standards, unutilized DTT channels in a given geographic area are referred to as TVWS (interleaved spectrum) and are assigned to CRN applications. Fig. 1 depicts DTT primary band coexistence with services in adjacent bands in the UHF band. Geolocation databases will be required to use the coexistence approach to protect existing users [5].

Fig. 1.

Illustration of UHF band Coexistence of Services [5].

Several challenges hinder this use of TVWS. Among them is the development of rules and regulations on how to make efficient use of the TVWS spectrum for non-broadcasting communication without causing interference to TV broadcasters and how can developing countries take advantage of the TVWS to benefit economically without being overtaken by multidimensional organizations. Furthermore, the fluctuating nature of the spectrum also makes it difficult for the regulatory authorities to formulate policies. This work can be made easier by the implementation of the cognitive radio network architecture that helps in the development of the network protocols to address dynamic spectrum sharing.

CRN has been presented as a solution to the inefficient use of radiofrequency [6]. Spectrum sensing is a key feature of CRN, and several studies have shown that cooperative spectrum sensing is the most widely utilized spectrum sensing technique for resolving the problem of interference from secondary users to main users [1,7]. The next generation of wireless technology, with convergent voice and data applications, has the potential to give rural broadband connectivity, giving Information and Communication Technology (ICT) enough impetus to play a part in all aspects of human activity. The availability of TVWS bands for cognitive access is one of the first real steps toward overcoming the spectrum scarcity problem in today's wireless networks, particularly in landlocked areas with limited access to fiber optic cables. Metaheuristic algorithms such as the firefly algorithm (FA), genetic algorithm (GA), and hybrid FAGA [8] have been applied to allocate spectrum but result in sub-optimal spectrum allocation due to either poor local search or global search or both [3]. The existing hybrid FAGA [9] for spectrum allocation can be improved by further hybridizing with other algorithms [10]. This article is aimed at developing a novel and improved resource allocation algorithm for a TVWS network based on a hybrid FAGAACO. The contribution of this paper is the development of a better method for spectrum allocation in a wireless TVWS network based on a Geo-Location Database (GLDB). FA was selected because of its demonstrated superiority concerning solution quality and convergence time [11]. FA can become locked in a local optimum despite surpassing other algorithms. FA uses the crossover feature of GA as well as the elements of ant colony optimization (ACO) to diversify the solution space search so that FA and ACO do not become stuck in the local optimum, thereby improving local search while GA-tweaked ACO enhances global search. As far as we know, FAGAACO has never been used for TVWS network spectrum allocation that uses GLDB. The simulation findings suggest that using FAGAACO improves total throughput and PU-SINR in a TVWS network. The rest of this paper was organized as follows. Section 2 discusses related work. Section 3 provided an overview of relevant algorithms. Section 4 describes a proposed FAGAACO technique. Sections 5 and 6 outline the system model based on CRN and the simulation setup. Section 7 discusses the performance of the hybrid FAGAACO, and Section 8 presents the paper's conclusion.

2. Related work

A hybrid firefly algorithm (FA), genetic algorithm (GA), and particle swarm optimization (FAGAPSO) has been employed in Ref. [10] to create a unique resource allocation technique for a TVWS network that takes into consideration adjacent channel interference as well as interference restrictions at both PUs and SUs. The hybrid FAGAPSO algorithm was developed for joint power and spectrum allocation in a GLDB-based wireless TVWS network where devices connect via a base station. FA was chosen from among other evolutionary algorithms because it surpasses others with regard to solution quality and convergence time [11]. However, it is still possible to get trapped in a local optimum.

Another study [12], recognized the inefficiencies of random allocation and improved their ACO technique for channel allocation as a result. Their primary concern was index throughput. They investigated a system with numerous heterogeneous CRNs and a fixed number of CRUs, PUs, and channel resources whose quantities vary dynamically depending on the number of contesting users and available vacant channels. To protect the PU from interference, they additionally assumed that the PU's channel-occupied pattern is static and aware. To improve the outcomes and convergence time for Traveling Salesman Problem (TSP), a practical combining technique for two evolutionary algorithms (FAACO) was developed based on ACO and FA [13]. Although ACO is used for global search to avoid local optimums, FA is utilized to identify the optimal solution based on local solutions. We prevent a local optimum while producing a better product in less time in this paper. This paper considered the low complexity nature of metaheuristic algorithms, therefore, presents a hybrid of FA, GA, and ACO in TVWS with a focus on the improvement of sum throughput, PU-SINR, and runtime. Furthermore, the tendency of metaheuristic algorithms of being trapped in local optimum was considered in this paper thus GA was introduced to tune FA and ACO.

3. Overview of related algorithms

This section includes an overview of the related algorithms FA, GA, and ACO, as well as the related hybrids.

3.1. Firefly algorithm

Yang devised the Firefly algorithm in 2008 [14], and it is founded on the idea that fireflies are unisexual, which means that all fireflies can be attractive to each other, and that attraction is proportionate to individual brightness levels. As a result, the brighter fireflies attract the less brilliant ones; nevertheless, if no fireflies are brighter than a specific firefly, it will migrate at random. The firefly algorithm's aim function is linked to the flashing light properties of the firefly population. Since the physical principle of light intensity is inversely quadratic proportional to the square of the area [15], this method can be utilized to develop an appropriate function for the distance between any two fireflies. Individuals are forced to migrate in the population in either a systematic or random fashion to optimize their fitness function. As a result, all fireflies will migrate to the ones with brighter flashing lights, until the colony congregates around the brightest one. To implement the firefly method, three parameters are used: attraction, randomization, and absorption. The attraction parameter is determined by the difference in light intensities between two fireflies. When the random walk associated with the Gaussian distribution principle's randomization parameter is set to zero, it behaves as if it were producing a number from an interval. When absorption parameters fluctuate from 0 to infinity, the value of attractiveness parameters changes. The movement of fireflies appears to be random in the case of infinity convergence.

Algorithm 1 shows the firefly optimization steps succinctly. The firefly technique has lately acquired prominence for solving difficulties that arise during the setup and operation of Resolution Enhanced Techniques (RETs). The firefly method is said to deal with multi-modal function formulations more effectively than other strategies based on its performance when compared to the well-known PSO and GA algorithms [16,17]. The following equation (1), (2) describe the fluctuation in attraction with distance r:

$$\beta ={\beta }_0{e}^{-\gamma r^2}\text{,}$$ (1)

where ${\beta }_0$ is the attractiveness at distance r = 0 and $\gamma$ is -------.

When a firefly $i$ is attracted to a brighter firefly $j$, the following factors are taken into account:

$$x_i^{t+1}=x_i^t+{\beta }_0{e}^{-\gamma }{r}_{i,j}^2(x_j^t-x_i^t)+{\alpha }_t{\epsilon }_i^t$$ (2)

where ${\alpha }_t$ is the randomization parameter and $x_i$ is -----.

${\mathbf{\epsilon }}_i^t$ is a vector of random numbers drawn from a random distribution at time $t$.

If ${\beta }_0$ = 0, this becomes a simple random walk.

Algorithm 1: Firefly Algorithm

Stage 1: Initialize the parameter values of FA: where $\gamma$ is light absorption coefficient, $\beta$ is Attractiveness, $\alpha$ is randomization parameter, maximum iterations $t_{\mathit{max}}$, fireflies number NP, while domain space D. Stage 2: Objective function definition f $\to \to$ = x1, x2, x3 ….., xn. and generation of the initial location of fireflies.; xi (i = 1,2 …..NP) while setting the iteration number to t = 0; Stage 3: while t $\le t_{\mathit{max}}\text{;}$  for i = 1 for NP (repeat for each individual sequentially);  for j = 1 for NP (repeat for each individual sequentially);  Compute light intensity ${\beta }_i$ as xi is determined by objective function f(xi);  If ${\beta }_i$ < ${\beta }_j$ then;  Move firefly i towards j according to equation (2);  End if;  Attractiveness varies with distance r via $e^{-rT}$ according to equation (1);  Estimate the new solutions then, update light intensity;  Check if the updated solutions are within limits;  End for  End for Stage 4: To get the current best, rank the fireflies

3.2. Genetic algorithm

Without any prior knowledge of the search region [10,18], Genetic Algorithms were used to determine the solution to a problem, which in most cases numerically solved it. To begin with, the chromosomes population is constructed to give possible solutions to the problem under consideration. The parent chromosomes are then crossed along to create a generation of new chromosomes. This is accomplished through the use of recombination and mutation operators. A fitness metric is used to assess the effectiveness of alternative solutions. Fitness solutions with higher levels of fitness will be granted the opportunity to reproduce more frequently. Algorithm 2 shows the genetic algorithm's essential structure.

Algorithm 2: Genetic Algorithm
Step 1: Generate the initial population of chromosomes Step 2: Compute the fitness of each chromosome Step 3: For i = 1 to N (number of iterations)  Perform a selection of parents to be crossed over  Perform crossover, then  Perform mutation, and finally  Find the fitness of each chromosome  End for

A random population generator generates the initial population of chromosomes, a fitness function to compute the fitness of each chromosome, and the selection, crossover, and mutation execution operators follow as the five key aspects of GA [18]. The chromosomes between the problem's lower and upper boundaries are specified by the random population generator. This set, also known as the first parents set, is in charge of producing the children of the next generation. Following the construction of the initial set, the fitness function is used to assess each chromosome's ability to solve the problem. The fitness function's functionality demonstrates that GA moves to the next stage when the selection operator chooses chromosomal pairing randomly as the next generation of chromosomes is reproduced. The crossover operator then enters the picture, picking a locus interval at random for each pair of chromosomes and swapping the subsequence inside that interval. However, some research has been conducted in trying to build a more advanced version of GA. To achieve this goal, various components should be updated, leading to a more convergent and speedier GA. In the formulation of GA, the synthesis problem needs a detailed consideration of the parameters impacting the initial population selection, crossover operator probability models, and mutating operators.

3.3. Ant colony optimization

The optimization of ACO is a population-based heuristic approach similar to Dorigo et al. PSO's technique. This strategy was inspired by the activities of ant colonies in their search for food. Each colony member in Refs. [19,20] strives to determine a well-worn channel through the food source. To establish their specific track for the source, the ants emit signaling pheromones. As the following ants prefer to travel down the route with the strongest pheromone, the pheromone level's saturation determines the likelihood of path selection. To communicate, ants use compounds known as pheromones. As they deposited pheromones on the ground, ants would leave a pheromone trail behind them. When other ants are present, they can detect pheromone trails and choose a path that will pass through the magnitude of likelihood. The ants then leave a pheromone trail, raising the amounts of pheromones along the path. As more ants follow the route, it becomes more tempting to follow. The probability of ants choosing a path grows as the number of ants choosing it climbs. Fig. 2 depicts the ants' movements.

$$\Delta {\mathbf{{\rm T}}}_{i,j}^k=\{\begin{array}{c}\frac{1}{L_k}\\ 0,\end{array}$$ (3)

where $k^{th}$ ant travel on the edge i,j and $L_k$ is the length of the path found by the $k^{th}$ ant.

$$T_{i,j}^K=\sum _{k=1}^m\Delta {\mathbf{{\rm T}}}_{i,j}^k\to withoutvaporization$$ (4)

$$T_{i,j}^K=(1-\rho )T_{i,j}+=\sum _{k=1}^m\Delta {\mathbf{{\rm T}}}_{i,j}^k\to withvaporization$$ (5)

Fig. 2.

Illustration of ants' movement [13].

where F and N are the terminals, a and b are paths taken by ants to and fro as they find food.

Algorithm 3: Ant Colony Optimization

1. Ants population and ACO parameter were initialized. 2. Channel was initialized as a city so as to lay the initial pheromone according to Equation (3). 3. Random placement of ants in the city was done according to Equation (15). 4. Then, the generation of random number q:  if q ≤ $q_0$ probability of the next city is:  $P_{i,j}^k$ = arg max (τ (i,j)). else, the probability of the next city is:  $P_{i,j}^k$ = ∑τ(i,j) τ(i,s) 5. ${\mathrm{k}}^{\mathrm{t}\mathrm{h}}$ ant deposits pheromones at the visited city. 6. The local pheromone update for all cities is done with Equation (4) with the application of Equations (14), (18), (19), (20). 7. When ${\mathrm{k}}^{\mathrm{t}\mathrm{h}}$ ant finishes a tour, then, assign channel matrix according to combination city by ant ${\mathrm{k}}^{\mathrm{t}\mathrm{h}}$. Else repeat step 4. 8. PU-SINR and sum throughput are calculated based on matrix tour according to Equation 6 9. When all ants accomplished the tour, the global pheromone update is based on the path of the best ant according to equation (5) with the application of Equations (14), (15), (16), and (17). 10. At the end of the ACO process, Determine the optimal solution for channel assignment according to Equation (8).

3.4. Hybrid firefly algorithm with ACO(FAACO)

FAACO [13] was proposed for solving [21] unconstrained optimization issues. Their objective for creating a new hybrid algorithm is to address a shortcoming of the original ant colony algorithm, which is inefficient for continuous optimization. They begin with ACO's meta-heuristic search [20], where groupings of possible variable values are created, with each value in the group having its trial information. The solutions are produced utilizing trial information at each iteration of ACO, while the firefly algorithm is used by others to increase the solution quality of optimization difficulties. Several distinguishing characteristics were acquired by the proposed method. To begin, the algorithm is launched by a group of random ants traversing the search space. As the ants move, they evolve by combining ACO and FA, with FA [22]serving as a local search to clarify the paths found by the ants. Second, as the optima strategy is used, the performance of the firefly is steadily increased by gradually decreasing the randomization parameter. This algorithm can be further improved by hybridizing it with other algorithms such as GA to investigate the performance of such a hybrid when they are not trapped in the local optimum.

3.5. Hybrid Firefly Algorithm and Genetic Algorithm (FAGA)

A hybrid FA and GA was proposed in Ref. [23]. All of the phases in the FA remain unchanged in this work, except that the two best solutions are crossed over for each iteration. From the four offspring, the two fittest are picked. One of the two offspring is chosen at random for mutation. When a chosen offspring produces a better result than the existing best solution, it will replace it. A binary optimization issue was solved using the technique. It is necessary to investigate the performance of the continuous optimization problem.

For the situation of the monoalphabetic substitution cipher [24] proposed, “a hybrid FA and GA. To move fireflies in space, the suggested algorithm makes use of genetic operators and the concept of dominant gene cross-over. During dominant gene cross-over, an offspring takes more from one parent than the other. These two could only improve exploitation but had a weak exploring ability.”

• 4.Hybrid FAGAACO Algorithm

Optimization algorithms such as FA, GA, and ACO have been employed on their own to allot spectrum, and some have been hybridized. However, they can become entrapped in a local optimum, resulting in suboptimal spectrum allocation. The purpose of this hybridization is to strengthen FA and ACO's exploitation and exploration abilities. This paper offers a novel hybrid FA, GA, and ACO with as few ants and fireflies as possible to achieve this goal. As shown in Algorithm 4, FA serves as the local search engine in this paper, whereas ACO is employed to find for global search [13,25]. First, because FA has fast convergence capacity, it is employed to locate a local search. After rating the fireflies based on their fitness levels in Equation (6), the first two best offspring are crossed to produce four new offspring. The purpose of performing the crossover is to keep FA from becoming trapped in a local optimum, through FA's exploration capabilities. The fitness ratings of the four new offspring are then ranked [3,26]. If the fitness values of the top four fireflies are higher, the chromosomes formed by crossing will be replaced. Vertical and horizontal crossover is used arbitrarily interchangeably. Normalize the firefly-generated local solutions by recognizing q different firefly visualizations as candidate tours. Fireflies with the same permutation solution are considered a single solution.

Secondly, we introduce GA operators to modify ACO parameters, preventing ACO from becoming stuck in a local optimum hence improving its global search because ACO has good exploration capabilities [13,21,27]. To create the initial pheromone trail, apply the pheromone to the edges that are part of the q candidate tours. The best solution normalization will result in the greatest pheromone addition near the edges. The second-best solution's margins receive less pheromone than the first's. As a result, the most frequently passed edges of the candidate tour will receive the most pheromone addition. ACO will be executed on this initial path. By building the initial trial, the number of agents and iterations for ACO will be minimized. As a result, ACO is implemented as a global search. As a result, the tour is as brief as feasible. This is shown in Algorithm 4 below.

Algorithm 4: FAGAACO

Step 1. Local Search by FA 1. Specify the number of SUs, N 2. Set the dimension of fireflies, D 3. Specify the number of fireflies as NP 4. Initialize the algorithm's control parameters such as $\alpha ,\beta ,\gamma$, number of firefly NP, and tmax,as maximum number of iterations. 5. Setting D, as the dimension of fireflies. 6. Do randomly assignment of each SU power values in between $pmin$ and $pmax$ 7. Random generation of the initial position for each firefly $xi$: 8. The fireflies are ranked with respect to their computed values of fitness according to Equation (14). 9. Find their current best solution. 10. Apply horizontal and vertical crossover interchangeably in a random manner to the first two best solutions. 11. If the fitness of the best offspring produced by crossover exceeds that of the present best, use it as the current best of FA. 12. Check firefly $xi$ to find if only one channel is assigned to each SU. If more one than channel is assigned to SU, randomly pick one of the channels and assign it to SU. 13. Move each firefly to the best solution using equation (2) and the applications of equations (18), (19), (20). 14. If the number of iterations reaches the predefined maximum, the spectrum allocation vector (A) for the current best solution is generated in stage 8 and the procedure is terminated; otherwise, return to step 6 and repeat. Step 2. Global Search by ACO 15. Initialized the ACO parameters 16. Initialized the population of ants to the final values of fireflies found in step 14. 17. Channel was initialized as a city so as to lay the initial pheromone according to Equation (3). 18. Random placement of ants in the city was done according to Equation (15). 19. q random number is generated when q ≤ $q_0$ then the probability of the next city is given as: $P_{i,j}^k$ = arg max $\left(\tau (\mathrm{i},\mathrm{j})\right)$. else, the probability of the next city is as given: $P_{i,j}^k$ = ∑τ(i,j) τ(i,s) 20. The ${\mathrm{k}}^{\mathrm{t}\mathrm{h}}$ ant deposit pheromones at every city visited. 21. The local pheromone update in all cities is done with Equation (4) with the application of Equations (14), (18), (19), (20). 22. When ${\mathrm{k}}^{\mathrm{t}\mathrm{h}}$ ant finishes a tour, then, assign channel matrix according to combination city by ant ${\mathrm{k}}^{\mathrm{t}\mathrm{h}}$. Else repeat step 19. 23. PU-SINR and sum throughput are calculated with regards to matrix tour according to Equation (6). 24. After completion of the tour, the global pheromone is updated based on the path of the best ant according to equation (5) with the application of Equations (14), (18), (19), (20). 25. At the tail end of the ACO process, determine the channel assignment's best solution according to Equation (8).

• 5.System Model, And Spectrum Allocation Using FAGAACO

In the network given in Fig. 3, a single TV receiver is displayed near the protective zone's edge. A TV receiver at this position is the most susceptible to interference of any TV receiver in the protection region due to its proximity to the secondary network and receipt of the weakest signal from the TV tower. According to GLDB regulations [5,11], the ratio of protection must be gauged near the edge of the protection region. Due to aggregate interference at the TV receiver, which includes both co-channel and surrounding channels, the protection ratio must not fall below the specified level.

Fig. 3.

Diagram for interference [10].

Spectrum allocation optimization is critical to limiting interference scenarios to the primary user (PU) and among secondary users (SUs). Let A = {a_n,m||a_n,m $\in$ {0,1} to represent the probable channel allocation matrix. Let the number of SUs be N, and let the number of channels be M, hence A has a dimension of NM. a_n,_m = 1, once user n is assigned to a channel m; a_n,_m = 0, once user n is not assigned to channel m. As a result, spectrum allocation works with binary variables, as opposed to power allocation, which deals with continuous quantities. The goal of the optimization is to find a channel allocation matrix A that maximizes the sum of all SU throughput in Equation (6).

$$\mathrm{U}=\sum _{n=1}^N\sum _{m=1}^M{r}_{n,m}$$ (6)

$${\mathrm{r}}_{\mathrm{n},\mathrm{m}}=1/2{\mathrm{a}}_{\mathrm{n},\mathrm{m}}{\mathrm{b}}_{\mathrm{m}}{\log }_2(1+{\rho }_2)$$ (7)

where b_m is the bandwidth, r_n,m is the throughput of the single SU transmitter, and is computed as per Equation (7).

The optimal channel allocation matrix can be achieved by solving the following optimization Problem 1 with its conditions.

Optimization Problem 1.

$$A^{*}=\mathit{arg}\mathit{max}U$$ (8)

Subject to:

$${\mathrm{C}}_1:\omega >{\omega }_0$$ (9)

$${\mathrm{C}}_2:{\rho }_n>{\rho }_0,\mathrm{n}=\mathrm{1,2,3}\dots \mathrm{N}$$ (10)

$${\mathrm{C}}_3:{\mathrm{a}}_{\mathrm{n},\mathrm{m}}\in \left\{\mathrm{1,0}\right\}\text{,}$$ (11)

$${\mathrm{C}}_4:{\mathrm{a}}_{\mathrm{n},\mathrm{m}}=1,{\mathrm{c}}_{\mathrm{n}}=\mathrm{m}\text{,}$$ (12)

$${\mathrm{C}}_5:{\mathrm{a}}_{\mathrm{n},\mathrm{m}}=0,{\mathrm{c}}_{\mathrm{n}}\ne \mathrm{m}\text{.}$$ (13)

Penalty functions are used to change the constrained optimization problem to unconstrained optimization which changes our objective function to Problem 2 with its conditions:

Optimization problem 2

$$\mathrm{Ф}\left(\mathrm{A}\right)=\mathrm{U}–{\mathrm{C}}_{\mathrm{s}}\sum _{n=1}^N\max [0\text{,}{g}_n^s]ˆ\left(2\right)-\mathrm{C}\_\left(\mathrm{p}\right)\max [0,g_n^p]ˆ\left(2\right)$$ (14)

Subject to:

$${\mathrm{C}}_3:{\mathrm{a}}_{\mathrm{n},\mathrm{m}}\in \left\{\mathrm{1,0}\right\}\text{,}$$ (15)

$${\mathrm{C}}_4:{\mathrm{a}}_{\mathrm{n},\mathrm{m}}=1,{\mathrm{c}}_{\mathrm{n}}=\mathrm{m}\text{,}$$ (16)

$${\mathrm{C}}_5:{\mathrm{a}}_{\mathrm{n},\mathrm{m}}=0,{\mathrm{c}}_{\mathrm{n}}\ne \mathrm{m}\text{.}$$ (17)

where Ф(A) is the objective function for sum throughput and C_s and C_p are penalty functions used to calculate the objective function.

Algorithm 4

demonstrates the procedures for applying FAGAACO to solve Optimization Problem 2. To begin, the program sets the number of fireflies to NP and the dimension of each firefly to D = N. Each firefly illustrates a different approach to determining the optimum spectrum allocation for all SUs in the TVWS network. Each firefly is a firefly-shaped channel allocation matrix. Each firefly will be granted the same amount of power as the SUs that are generated at random. During any of the activities, the power assignment will remain constant. The best firefly is chosen at each iteration, and each firefly movement is carried out in line with Algorithm 4 Step 1.

$${\mathrm{r}}_{\mathrm{i},\mathrm{j}=}\sum _{d=1}^D\sum _{m=1}^M{x}_{m,d,i}⨂x_{m,d,j}$$ (18)

where $x_{m,d,i}$ and $x_{m,d,j}$ are firefly i and j channel allocation values at m and d places in the channel allocation matrix because the channel allocation matrix is made up of binary values. Equation (14) is applied to it, and firefly movement produces non-binary data. To determine whether $x_{m,d,j}$ will be a 0 or a 1, use the Sigmoid function to alter the value following the ant mobility, as illustrated in equation (16) below:

$$\mathrm{s}\mathrm{i}\mathrm{g}\left(x_{m,d,i}\right)=\frac{1}{1+e^{{-x}_{m,d,i}}}\text{,}$$ (19)

For the calculation of the value of every position in the channel allocation matrix, the following formula is used.

$$x_{m,d,i}^{t+1}=\{\begin{array}{c}1,\mathrm{r}\mathrm{a}\mathrm{n}\mathrm{d}\left(\right)<\mathrm{s}\mathrm{i}\mathrm{g}\left(\mathrm{f}\right)\\ 0,else\end{array}$$ (20)

where f = $x_{m,d,i}^t$

After a certain amount of iterations, the firefly with the best objective function is chosen as the solution to the spectrum allocation problem. The top two best selections are then subjected to horizontal and vertical crossover in random order. If the fitness of the best offspring produced by crossover exceeds that of the present best, use it as the current best solution for FA. Using equations (2), (18), (19), (20), move each firefly to the optimal solution (20). If the number of iterations reaches the predefined maximum, the current best solution's spectrum allocation vector (A) is created.

The ant population is initialized as per the final value of fireflies in step (14) of Algorithm 4. According to Equation (14), the channels are initiated as a city to lay the initial pheromone, set ant in a random city, and generate a random number q using Equation (18):

if q ≤ $q_0$ probability of the next city is given in Equation (21):

$$P_{i,j}^k=\arg \max (\tau \left(\mathrm{i}\mathrm{j}\right))$$ (21)

else, the probability of the next city is given in Equation (22):

$$P_{i,j}^k=\sum \tau (\mathrm{i},\mathrm{j})\tau (\mathrm{i},\mathrm{s})$$ (22)

Ant ${\mathrm{k}}^{\mathrm{t}\mathrm{h}}$ deposits pheromone in the visited city and locally updates pheromone for all cities using Equation (4) as well as Equations (14), (18), (19), (20). If ant ${\mathrm{k}}^{\mathrm{t}\mathrm{h}}$ completes a tour, allocates vector channel based on ant ${\mathrm{k}}^{\mathrm{t}\mathrm{h}}$'s combination city, else repeat step 4. Calculate SINR and throughput using Equation 6's matrix tour, and sum throughput using Equation (6).

If all ants complete the tour, the global update pheromone is based on the path of the best ant as determined by equation (5), as well as Equations (14), (18), (19), (20). Get the optimal solution for channel assignment using Equation (8) at the end of the ACO procedure.

6. Simulation system set up

MATLAB R2018a was used for the simulation. MATLAB was chosen because it has a large number of built-in functions. Fig. 2 depicts the MATLAB network diagram. A 1 sq. km region is covered by 1000 SUs. SUs were randomly dispersed among 10 channels. The channels used in this were those from the Nairobi Central Business District (CBD). Fig. 4 is the MATLAB's network diagram. The algorithm was in two steps as shown in Algorithm 4 below.

Algorithm 4: FAGAACO

Step 1. Local Search by FA 1. Specify the number of SUs, N 2. Set the dimension of fireflies, D 3. Specify the number of fireflies as NP 4. Initialize the algorithm's control parameters such as $\alpha ,\beta ,\gamma$, number of firefly NP, and tmax,as maximum number of iterations. 5. Setting D, as the dimension of fireflies. 6. Do randomly assignment of each SU power values in between $pmin$ and $pmax$ 7. Random generation of the initial position for each firefly $xi$: 8. The fireflies are ranked with respect to their computed values of fitness according to Equation (14). 9. Find their current best solution. 10. Apply horizontal and vertical crossover interchangeably in a random manner to the first two best solutions. 11. If the fitness of the best offspring produced by crossover exceeds that of the present best, use it as the current best of FA. 12. Check firefly $xi$ to find if only one channel is assigned to each SU. If more one than channel is assigned to SU, randomly pick one of the channels and assign it to SU. 13. Move each firefly to the best solution using equation (2) and the applications of Equations (18), (19), (20). 14. If the number of iterations reaches the predefined maximum, the spectrum allocation vector (A) for the current best solution is generated in stage 8 and the procedure is terminated; otherwise, return to step 6 and repeat. Step 2. Global Search by ACO 15. Initialized the ACO parameters 16. Initialized the population of ants to the final values of fireflies found in step 14. 17. Channel was initialized as a city so as to lay the initial pheromone according to Equation (3). 18. Random placement of ants in the city was done according to Equation (15). 19. q random number is generated when q ≤ $q_0$ then the probability of the next city is given as: $P_{i,j}^k$ = arg max (τ (ij)). else, the probability of the next city is as given: $P_{i,j}^k$ = ∑τ(i,j) τ(i,s) 20. The ${\mathrm{k}}^{\mathrm{t}\mathrm{h}}$ ant deposite pheromones at every city visited. 21. The local pheromone update in all cities is done with Equation (4) with application of Equations (14), (18), (19), (20). 22. When ${\mathrm{k}}^{\mathrm{t}\mathrm{h}}$ ant finishes a tour, then, assign vector channel according to combination city by ant ${\mathrm{k}}^{\mathrm{t}\mathrm{h}}$. Else repeat step 19. 23. PU-SINR and sum throughput are calculated with regards to matrix tour according to Equation (6). 24. After completion of the tour, global pheromone is updated based on the path of the best ant according to equation (5) with the application of Equations (14), (18), (19), (20). 25. At the tail end of the ACO process, determine the channel assignment's best solution according to Equation (8).

Fig. 4.

Network Diagram [10].

The initial channel assignment is also made at random.

The path loss was modeled using the free space path loss model [28] in Equation (23):

$$\mathrm{P}\left(\mathrm{d}\right)=20\log \left(\mathrm{d}\right)+20\log \left(\mathrm{f}\right)-147.55$$ (23)

Whereby in this case d represents the distance in meters whereas f represents the operating frequency. After that, the proposed spectrum allocation mechanism is used to allot the SUs channels. Table 1 lists the MATLAB simulation parameters that were used during the simulation process. The following are the FA parameters:

Table 1.

Parameters for simulation.

Parameter	Value	Description
${\mathit{b}}_{\mathit{m}}$	6 Megahertz	TV channel Bandwidth (BW)
${\mathit{f}}_{\mathit{a}}$	650 Megahertz	DTV signal Centre Frequency
${\mathit{P}}_{\mathit{T}\mathit{V}}$	−70.6 dB mW	Power of DTV signal at victim TV receiver
${\mathit{\delta }}_{\mathit{n}}^{\mathbf{2}}$	−102 dB mW	The noise power
${\mathit{\omega }}_{\mathbf{0}}$	23 dB	The threshold for TV receiver SINR
${\mathit{\rho }}_{\mathbf{0}}$	7 dB	The threshold for SU SINR
${\mathit{P}}^{\mathit{B}\mathit{S}}$	36 dB mW	The base station transmits power
${\mathit{P}}_{\mathit{max}}$	30 dB mW	The Max SU transmits power
$\mu ({\mathit{c}}_{\mathit{T}\mathit{V}},{\mathit{c}}_{\mathit{n}})$	0, −28 dB	co-efficient for adjacent channel interference
${\mathit{G}}_{\mathit{S}\mathit{U}}$	10 dB	Antenna gain for SU
${\mathit{G}}_{\mathit{P}\mathit{U}}$	10 dB	Antenna gain for PU
${\mathit{G}}_{\mathit{B}\mathit{S}}$	10 dB	antenna gain for Access point
Q	1	ACO Parameter
ρ	0.1	ACO Parameter
β	0.5	ACO Parameter
N	20	Number of ants
${\mathit{Q}}_{\mathbf{0}}$	0.6	ACO Parameter

${\beta }_0$=1, $\alpha$ = 30, $\gamma$ = 10, number of fireflies $\mathrm{N}$ = 50.

GA parameters are the Number of chromosomes $\mathrm{N}$ = 50, the rate of mutation = 0.8 while the rate of selection = 0.5 whereas the ACO parameters are as follows: $\mathrm{Q}$ = 1, $\mathrm{Q}\mathrm{o}$ = 0.6, $\delta$ = 0.5, $\rho$ = 0.1, number of ants N = 50. For ACO, GA, and FA, 150 maximum number of iterations were used and the total number of runs was 10, and the average was done on throughput, PU SINR, runtime, and convergence time.

7. Simulation results and discussion

This section contains simulation findings for FAGAACO-based spectrum allocation optimization. The suggested method is compared against FA, ACO, GA, and FAGA. The simulation results are averaged over ten simulation runs. The following measures are used to evaluate the performances of the algorithm.

• •The algorithm running time,
• •The objective function value,
• •Sum throughput, and
• •PU SINR.

The presented results for N = 500 are different from the results for N = 1000. This is so because of network density. When N = 500, there is less interference compared to when N = 1000 thus creating the difference in PU SINR and Sum throughput.

7.1. Sum throughput analysis

In terms of sum throughput in Gbps, Table 2 below compares the three algorithms, a hybrid of firefly and genetic algorithms and a hybrid FAGAACO. For M = 500, FAGAACO's total throughput is 19.72%, 16.51%, 13.03, and 7.62% higher than FA, GA, FAGA, and ACO respectively. For M = 1000, FAGA-ACO's total throughput is 16.66%, 13.71%, 10.55%, and 4.44% higher than FA, GA, FAGA, and ACO, respectively. These results indicate that FAGAACO performs better than the other algorithms in terms of throughput. This is because FAGAACO results in more optimal spectrum allocation, which reduces/lowers interference and thus maximizes throughput. The improvement in sum throughput is because FA's exploration abilities have been improved further by the addition of the crossover chromosomes of GA. Further addition of ACO which has good global search made this hybrid algorithm perform more efficiently than the other metaheuristic algorithms.

Table 2.

Comparison of sum throughput.

No of SUs	Algorithm	Sum Throughput (Gbps)	Percentage of improvement by FAGAACO
500	FA	6.1918	19.72%
	GA	6.4390	16.51%
	FAGA	6.7079	13.03%
	ACO	7.1247	7.62%
	FAGAACO	7.7125
1000	FA	6.4703	16.66%
	GA	6.6990	13.71%
	FAGA	6.9447	10.55%
	ACO	7.4192	4.44%
	FAGAACO	7.7637

7.2. Pu sinr analysis

Table 3 compares the FAGAACO algorithm's performance to that of other algorithms in relation to PU SINR. For M = 500 and M = 1000, the PU near the edge of the protection region is entirely protected. In terms of PU SINR, the results reveal that there is no substantial difference in performance between FAGAACO and the other algorithms. This is partly because the PU penalty period is so short compared to the other terms. Table 3. Comparison of PU SINR for different algorithms.

Table 3.

Comparison of Pu sinr with different algorithms.

No of SUs	Algorithm	PU SINR (db)	Percentage improvement by ACO.
500	FA	13.8986	−28.33%
	GA	18.8615	−73.88%
	FAGA	22.0615	−104.06%
	ACO	17.112	−58.28%
	FAGAACO	10.8108
1000	FA	14.7334	−209.23%
	GA	−13.6379	1.1%
	FAGA	11.3487	−184.1%
	ACO	7.5713	−156.1%
	FAGAACO	−13.4882

7.3. Running time

Table 4 shows the comparison of the running time of FAGAACO to that of other algorithms. 50 SUs in a network were considered for the results in Table 4 below. The results indicate that FAGAACO has a slightly longer runtime than FA and ACO while ACO has the shortest runtime. This is so because the tuning using GA occurs severally to find the best parameters. To have good accuracy, you may experience worse runtime which could improve once training is complete. Another reason why FAGAACO has a longer running time than FA, ACO, and FAGA is that the iterations number used for FAGAACO is half (50), that of FA, FAGA, and ACO and the added features of ACO and GA into pure FA.

Table 4.

Comparison of runtime for different algorithms.

Algorithm	Runtime (seconds)	Percentage improvement by FAGAACO.
FA	5.9304	12.8%
GA	9.6261	−41.54%
FAGA	6.4588	5.03%
ACO	5.1141	24.8%
FAGAACO	6.8012

The computer specifications for running the simulations are as follows: Windows 10 64-bit operating system, 8 GB RAM, and a 2.80 GHz dual-core processor The function timeit repeatedly calls a measured function and then returns the median of the computed running time for a measured function.

7.4. Objective function value

Table 5 below shows the comparison of the objective function value of the proposed algorithm against other algorithms for N = 500. The results show that FAGAACO has the best objective function value over the other algorithms. In this, the penalty functions are subtracted as shown in optimization problem 2. Since the values of the penalty functions are very minimal, the difference between the sum throughput and objective function values is very small.

Table 5.

Comparison of the objective function value.

No of SUs	Algorithm	Objective Function Value	Percentage improvement by FAGAACO.
500	FA	6142	14.7%
	GA	6676	7.3%
	FAGA	7110	1.3%
	ACO	7139	0.8%
	FAGAACO	7200

8. Performance evaluation of the FAGAACO algorithm

Spectrum allocation in TVWS is a binary optimization problem. From the simulation results presented in the above sections, this optimization problem in FAGAACO outperformed FA, GA, ACO, and FAGA with respect to the objective function value, the sum throughput, and the PU SINR. However, due to the addition of GA operators in tuning both FA and ACO parameters, the runtime of the proposed algorithm was slightly increased. Comparing the performances of the algorithms in consideration, it is clear that the exploitation and exploration abilities of FA, and ACO were improved therefore improving the overall performances of the proposed algorithm.

9. Conclusion

This paper presented a novel hybrid algorithm featuring the other three algorithms in the likes of ant colony optimization algorithm, genetic algorithm, and firefly algorithm for spectrum allocation in TVWS networks. Simulation results indicate that the proposed algorithm FAGAACO achieved the best sum throughput, objective function value, and PU SINR. The addition of GA operators to tune both FA and ACO parameters increased runtime for FAGAACO. Future work shall analyze the relationship between runtime and complexity.

Author contribution statement

Jacob Bol Mach Chol: Conceived and designed the experiments; Performed the experiments; Analyzed and interpreted the data; Contributed reagents, materials, analysis tools or data; Wrote the paper.Kennedy K. Ronoh: Conceived and designed the experiments; Analyzed and interpreted the data; Contributed reagents, materials, analysis tools or data; Wrote the paper.Kibet Langat: Analyzed and interpreted the data; Contributed reagents, materials, analysis tools or data; Wrote the paper.

Funding statement

Jacob Bol Mach Chol was supported by Pan African University Institute for Basic Sciences, Technology and Innovation (PAUSTI), Kenya.

Data availability statement

The data that has been used is confidential.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.