A Novel Metaheuristic Optimization for Throughput Maximization in Energy Harvesting Cognitive Radio Network

1 Abstract —In this article, a novel technique is proposed, namely rank-based multi-objective antlion optimization (RMOALO), and applied to optimize the performance of the energy harvesting cognitive radio network (EHCRN). The original selection method in multi-objective antlion optimizer (MOALO) is suitably changed to improve the algorithm, thus reaching the optimal solution for the problem. The proposed technique shows considerable performance improvement over the method used in the multi-objective antlion optimizer (MOALO). The performance of the proposed RMOALO is demonstrated on five benchmark mathematical functions and compared to multi-objective particle swarm optimization (MOPSO), multi-objective moth flame optimization (MOMFO), MOALO-Tournament, and MOALO-Roulette. The simulation results show an improved convergence of RMOALO and find the optimal solution to the throughput maximization problem. We show that RMOALO provides 16.33 % improved average throughput with the optimal value of sensing duration for the varying amount of harvested energy compared to MOPSO, MOMFO, MOALO-Roulette, and MOALO-Tournament.


I. INTRODUCTION
The demand and popularity of efficient wireless networks have increased over the past decade. Cognitive radio (CR) has been shown to be an emerging technology in wireless networks [1]. Cognitive radios are battery-operated with a limited network lifetime [2], [3]. With the advent of new devices, the efficient use of spectrum and energy has become a concern for most researchers. Energy harvesting is a promising addition to cognitive radio networks (CRN) to save energy and maximize throughput in next-generation wireless networks [4]. Energy harvesting is achieved from different energy sources in an energy harvesting cognitive radio network (EHCRN). The sources of energy in [5] are ambient such as solar, wind, motion, etc. from where the energy is harvested. The cognitive radio system uses ambient energy sources in [6], [7]. The RF (radio frequency) signal utilized by the secondary network acts as a source depending on the state of the channel in [8].
To meet the aforementioned challenges, optimization of the parameters that affect the performance of the energy harvesting cognitive radio network is considered [9]. To efficiently utilize the energy harvesting from the primary transmitter (PT), both energy harvesting and information transfer can be accomplished using the separated spectrum sensing and energy harvesting scheme (SSSEH). It can improve wireless network throughput, sensing time, and reduce the risk of collision between the primary transmitter and the primary receiver.

II. RELATED WORKS
For the EHCRN in [10], the average throughput of the secondary network is maximized by an optimal pairing of the sensing duration and the energy detector sensing threshold. In [11], a hidden Markov model describes the imperfect spectrum sensing process. The network obtains the optimal solution while adapting its parameters based on quality of service (QoS) requirements [12]. Some previous works have maximized throughput by optimizing resource allocation between primary and secondary users [13]. To maximize the throughput of the secondary user, optimal spectrum sensing energy, the transmit energy, and spectrum sensing interval Markov decision process (MDP) framework is used in [14]. In [15], optimized sensing time is achieved to improve the throughput in CR with a trade-off between the two. The optimization problem solved in [16] with the energy constraint and the collision constraint maximizes the total throughput of the secondary network in which the ambient source has been used for harvesting. Optimization of sensing threshold and sensing duration jointly for throughput maximization of a CRN is studied in [17]. The throughput of CRN is maximized by maintaining a proper trade-off between the harvested energy and the transmission of data with an optimal transmission time for primary and secondary users in [18]. In [19], the harvesting interval and the transmission interval are optimized to maximize the total achievable throughput of cognitive radio networks to obtain the maximum total achievable throughput. The sensing interval problem of the idle and busy channels in the EHbased CR network was formulated in [20]. A Markov chain was developed to find the energy state transition probability to solve the energy wastage problem.
From the literature, it is seen that spectrum sensing optimization has been extensively studied, and most of the researchers emphasized optimizing the trade-off for spectrum sensing and throughput in EHCRN by solving it as a convex optimization problem [18]- [20]. Despite the advances mentioned above, there is still a trade-off between throughput and sensing in EHCRN with constraints on interference and energy [21]. For example, the CR needs to sense the spectrum with the minimum energy in less time to get overall maximum throughput. These problems are solved using classical optimization techniques. These existing optimization methods incorporate high complexity if the problem has a trade-off and multiple parameters to be handled simultaneously. Constrained optimization problems are more challenging to solve than unconstrained optimization. Such constraints and trade-offs can be dealt with using metaheuristic-based multi-objective optimization, as it provides an optimal solution by optimizing two or more objectives simultaneously. Moreover, these techniques offer faster convergence and provide global solutions efficiently. Although in the literature [22], the issues of efficient resource utilization are solved using dynamic programming or mixed-integer nonlinear programming (MNLP) but with a high computational cost.
For cognitive radio network (CRN), up to the authors knowledge, metaheuristic-based multi-objective optimization methods have been used in related topics in [23]- [25] and have given satisfactory results, but we are not sure about separated spectrum sensing and energy harvesting scenario (SSSEH) in energy harvesting cognitive radio networks where energy harvesting and spectrum sensing occur separately in particular. Motivated by the works mentioned above, the focus of our work is to improve the performance of an energy harvesting cognitive radio network with the maximum throughput requirement while satisfying energy and interference constraints. This is achieved by multi-objective optimization of the EHCRN using the proposed novel metaheuristic technique. Constrained optimization can be a great solution to existing spectrum and energy problems. Analytical expressions for throughput and energy ratio are developed under the separated spectrum sensing and energy harvesting (SSSEH) scenario. The performance comparison of throughput under parameters similar to the baseline technique proposed in [26] is made. The impact of interference, signal-to-noise ratio (SNR), and harvested energy on throughput is also studied.
We have implemented the optimization problem of throughput maximization using multi-objective particle swarm optimization (MOPSO) [27], multi-objective moth flame optimization (MOMFO) [28], multi-objective antlion optimization (MOALO)-Roulette and MAOLO-Tournament [29] in the separated spectrum sensing and energy harvesting (SSSEH) scenario. These optimization techniques lack the proper trade-off between their intensification and diversification processes and get stuck to the best local solution.
Thus, we propose a rank-based multi-objective antlion optimization algorithm (RMOALO), which can prevent the solution from getting stuck in the local optimum to find the global optimal sensing time, maximizing the average throughput. Additionally, RMOALO is tested for various benchmark functions to validate its effectiveness. Apart from this, the performance comparison of the proposed algorithm with other metaheuristic algorithms shows that RMOALO outperforms in reaching the optimal solution. The comparison helps to find the best suitable algorithm for the given problem. The key contributions of this research work are summarized as follows: 1. Formulation of throughput maximization as a nonconvex optimization problem using the novel fitness function for average throughput in separated spectrum sensing and energy harvesting (SSSEH) scenario.
2. An improved rank-based multi-objective metaheuristic optimization algorithm is proposed and used to find an efficient global solution. The benchmarking of the proposed algorithm with the state-of-the-art metaheuristic algorithms is also done. 3. The simulated results compared with the conventional scheme demonstrate that the proposed metaheuristic algorithm substantially increases the throughput of the secondary transmitter (ST). The rest of the paper is organized as follows. Section III introduces the system model of the separated spectrum sensing and energy harvesting scheme (SSSEH) in EHCRN. For the network's maximum throughput demand, the multiobjective optimization problem for throughput maximization is formulated in Section IV. A novel multi-objective algorithm is proposed to obtain the optimal sensing duration in Section V. Section VI presents the simulated results and discussions. Section VII concludes the paper and presents future work.

III. SYSTEM MODEL
The system model of CR equipped with wireless energy harvesting for separated spectrum sensing and energy harvesting (SSSEH) is illustrated in Fig. 1. It consists of a primary and secondary network. The primary network consists of the primary transmitter-receiver pair and the secondary network consists of a secondary transmitter-receiver pair. The secondary transmitter (ST) is equipped with an RF energy harvester consisting of a rectifier unit and a rechargeable battery. The ST uses harvest-store-use for guaranteed QoS [30]. The primary network uses a licensed spectrum and has a fixed power source. Primary transmitter and receiver use synchronous slotted communication with the duration of the slot "T". The secondary network is not licensed to use the spectrum, but opportunistically accesses the licensed user's spectrum depending upon the availability of the primary user. The ST senses the spectrum periodically according to the spectrum state of (H 0 or H 1 ) to harvest energy, signal sensing, and data transmission. H 0 gives the primary receiver state as an idle spectrum state and H 1 as an occupied spectrum state. The frame structure of SSSEH is illustrated using Fig. 2

IV. PROBLEM FORMULATION FOR MULTI-OBJECTIVE OPTIMIZATION
This section aims to formulate a fitness function for throughput maximization and the energy ratio at the secondary transmitter (ST).

A. Energy Harvesting and Consumption
The energy harvester in the secondary transmitter harvests energy from the RF signal of the primary transmitter if there is no user signal. As shown in Fig. 2, each frame duration is "T" and the energy arrival is random, with P h as the average rate. In the harvesting slot, the average harvested energy is given as E h = P h τ 1 , which is available to the ST in the sensing slot. The secondary transmitter executes spectrum sensing operation using energy detection and consuming energy E s = e s τ 2 in the sensing phase, where e s is the power required for spectrum sensing. The assumption made in this model is that the energy harvested in different harvesting timeslots is not dependent on the channel between the primary transmitter and the RF energy harvester.
The Markov process is used to model the state occupation of the channel [32]. The sensing results of the channel being occupied or idle are given by the channel occupation state as θ n  {0 (idle), 1 (occupied)} for the slot n. The state transition probabilities with the channel occupancy state are illustrated in Fig. 3. Here, the probability of transit is q i for the idle state and q o for the occupied state. Thus, the steady-state probabilities are given by 1 2 respectively [17], with .  0 1 i  Let e t represent the power required for data transmission. If the secondary transmitter finds the spectrum occupied, i.e., θ n = 1, it starts harvesting the energy from the primary transmitter but does not consume energy for data transmission. If the channel is idle, i.e., θ n = 0, the secondary transmitter consumes E t = e t (T -τ 1 -τ 2 ) (1 -θ n ) energy during the transmission phase. Thus, the expression for the average energy consumed in slot n at ST is Energy consumption should not exceed the amount of harvested energy, i.e., E c ≤ E h , in each slot, since the harvested energy depends on the availability of the primary transmitter signal, so the energy constraint is considered to meet the power required for sensing and transmission.
When the secondary transmitter is active and the primary channel is idle, the novel fitness function derived from the energy ratio in terms of the average energy harvested into the average energy consumption is given as Energy consumption and spectrum sensing are intertwined, since ST consumes energy during the sensing phase. So, it becomes essential to consider the restrictions on energy consumption for sensing in the separated spectrum sensing and energy harvesting (SSSEH).

B. Optimization of Sensing Duration for Throughput
Maximization Spectrum sensing is performed by the secondary transmitter with energy detection of the RF signal periodically in the duration of the slot "T". It is also assumed that the secondary transmitter has enough data for transmission. The following hypothesis is considered to detect whether the spectrum is occupied or idle where H 0 and H 1 give the channel state (occupied or idle), respectively, y n (m) is the m th sample of the energy detector in a slot "n", s(m) represents the signal of the primary transmitter, and w(m) represents the noise, respectively. Both are random processes that are supposed to be independent circularly symmetric complex Gaussian (CSCG) with respective variances σ 2 p and σ 2 w . To optimize the sensing duration τ 2 in the SSSEH scenario, the sensing performance is given in terms of the false alarm probability P f ( , ), 2  and signal detection probability P d ( , ) 2 : where Q(x) represents the standard q function, ε ∈ R+ represents the threshold where R+ denotes the set of nonnegative real numbers, and f s represents the sampling frequency. The number of samples in the sensing slot is τ 2 f s . As the secondary transmitter harvests the RF energy from the primary transmitter, there is a likelihood of collision between the primary and secondary transmitters.
Case I Primary network is idle. Let P nc (τ 2 , ε, P h ) denote the probability of no collision while sensing when the primary channel used by the primary network is idle. The throughput of the secondary network when the primary network is idle is where s  is signal-tonoise ratio at the input of the secondary transmitter 2 2 2 ( , , ) ( , , )(1 ( , )), sh PP  is the probability of the secondary transmitter being active. The system is considered active from a long-term perception. There is an upper bound on the activation probability in SSSEH given by 22 12 ( , , ) ( , , ) Case II Primary network is occupied. Let P c (τ 2 , ε, P h ) denote the probability of collision while sensing when the primary channel is occupied. The throughput of the secondary network when the channel is occupied is The received signal-to-noise ratio in the secondary network for secondary and primary signals is γ s and γ p , respectively The average throughput of the ST depends on the probability that the secondary transmitter transmits without collision and in the presence of collision. Thus, the normalized average throughput R s using (6) and (7) is given as Protection of the licensed user, i.e., the primary receiver, is of utmost importance. So, when the channel of the primary network is occupied, the collision probability should be less than its target value where Ptc is the target collision probability of protecting the primary network. Here, the sensing duration is a crucial term to which throughput maximization is achieved. Therefore, the novel fitness function used for sensing duration optimization is formulated as To maximize the fitness function in (11), the rank-based multi-objective optimization (RMOALO) is proposed to optimize the sensing duation and solve the problem of throughput maximization in the given optimization problem.
 Evaluate each of the particles in the population and store the position of the particles in the population representing non-dominated solutions and leaders in the repository (rep).  Initialize the memory of each particle that guides it to travel through the search space. This memory is also stored in the repository.  The velocity of a particle "i" is based on the best position already fetched by the particle, pbest[i], and the best position already fetched by the set of neighbors of "i", rep, which is a leader of the repository 12 The coefficient IW is the particle inertia that controls how much the previous velocity affects the current one and takes a value of 0.4; r 1 and r 2 are random numbers in the range [0…1]. If the new position and the current pbest[i] are nondominated, the new value is chosen randomly between these two vectors. rep[h] is a particle from the repository, chosen as a guide for i.
As there are many best solutions from which the fittest one should be chosen, but due to lack of exploitation, MOPSO is incapable of searching globally. Therefore, it converges early without finding the fittest solution. Hence, we tend to solve the problem with the MOMFO algorithm.

B. Multi-Objective Moth Flame Optimization
MOMFO has modified Moth flame optimization [33] that includes the following steps.
 Initialize the position of "i" number of "m" moths and "j" number of "f" flames.
where S designates a spiral function which permits each moth to fly around a flame; it is not clear that the moth has to fly in the space between the moth position and the flame. It can also discover the other space. Therefore, there is a more efficient exploration and exploitation of the search space by moths where d i is the absolute distance |f j −m i |, b is the constant for controlling the shape of the logarithmic spiral function, t is a random number between [-1, 1]. Furthermore, the reduction in number of flames N f is adaptive and is reduced with respect to the increase in iteration where N fmax is the maximum number of flames. The MOMFO has the capability to reach the best solution due to efficient exploration and exploitation of the search space as this algorithm updates the position based upon the absolute distance between moth and flame.

C. Multi-Objective Antlion Optimizer (MOALO)
MOALO is the extended version of Antlion Optimization (ALO) and follows the same search behavior as ALO. It is inspired by the unique hunting behavior of antlions. Antlions are net-winged insects, and the chosen prey are ants. Antlions form the cone-shaped trap in the sand for ants while throwing out the sand [34].
Mathematical Modeling of MOALO. The mathematical modeling of hunting includes five different steps: search agents with random walk, trap formation, trap ants, catching prey, trap reconstruction, and elitism [35].
Random walk of search agents. The search for food makes the ants move stochastically over the search space. The hunting process of antlions is modeled by the interaction of the antlions with the ants modeled by random walk as The cumulative sum is calculated by cumsum with the maximum number of iterations as max-iter and r(t) as a stochastic function, and t indicates the random walk step, and the rand is any number between 0 and 1 1 0.5, The steps of the ant should be within defined boundaries, so where a i and b i signify the i-th ant variable showing the minimum and maximum random walk. For each iteration, , where c t and d t are the minimum and maximum of all the variables in the t-th iteration, where I is a ratio for controlling the radius, c t and d t is the minimum and maximum of all the variables at the t-th iteration.
The ratio 1 10 , w t I T


where t represents the current iteration, T is the maximum number of iterations, and w is defined based on the current iteration.
Catching prey and reconstruction of the pit. The prey caught (ant) at the bottom of the pit becomes fitter than its corresponding antlion. An antlion is then required to update its position to the latest position of the hunted ant to catch new prey in the next iterations. The following equation simulates this Here, t denotes the current iteration and  where t A R is the random walk around the antlion in iteration t, and t E R is the random walk around the elite in iteration t. Here, the roulette wheel is used to select the random walk.
The archive is updated with the solutions explored in the next iteration. The selected solution is based on the probability using the equation as follows The probability with which the solution is removed from the archive is as follows Here, N i represents the number of solutions for the i-th solution in the neighborhood, and c is a constant with a value greater than 1.
As MOALO gives diverse new solutions having very close values, it is necessary to handle this behavior with a suitable algorithm.

D. Proposed Novel Rank-based Multi-Objective Antlion Optimization (RMOALO)
The strength of a metaheuristic algorithm on a given optimization problem is determined by its ability to provide a balance between the global search and the local search. The proposed algorithm (see Algorithm 1) uses rank-based selection instead of the roulette wheel selection used in MOALO. To prove the competence of this selection method, we have also implemented MOALO with a tournament-based selection method. Tournament selection is used in one of the variants of antlion optimization (ALO) [36]. MOALO uses a repository to store non-dominated Pareto optimal solutions obtained at a given point in time. Solutions are then chosen from this repository using a roulette wheel mechanism based on the coverage of solutions as antlions to guide ants towards promising regions of multi-objective search spaces. The selection probability of all individuals becomes almost identical, which works against the basic idea of genetic algorithms. Thus, we proposed the algorithm, which is named a "rankbased multi-objective optimization algorithm" (RMOALO). Rank-based selection involves sorting all the random walks in decreasing order, arranging them in a queue, and moving towards the antlions from the higher-order rank to the lower one. Therefore, the position of ants in (25) updated using a roulette wheel is modified to rank selection, helping to faster convergence. Thus, the arrangement of random walk of ants is listed in decreasing order and ranked accordingly followed by the rank of ants: Relating the metaheuristic technique to the fitness function is essential for understanding the behavior of the problem and solution. Similarly to the mapping done between the algorithm based on swarm intelligence and energy-efficient CR in [37], the correlation between the metaheuristic algorithms and the fitness function becomes important (see the data in Table II below).

VI. SIMULATION RESULTS AND DISCUSSION
In this section, the throughput analysis for the separated spectrum sensing and energy harvesting scenario for the EHCRN with the proposed algorithm is confirmed by means of MATLAB simulations. The implementation was performed on a machine running the Windows 10 operating system version 21H1. It has an installed RAM of 8 GB using 11th Gen Intel(R) Core(TM) i5-1135G7 @ 2.40 GHz 1.38 GHz, 64 Bit Processor. For simulation purposes, the system parameters used are mainly derived from [14] (as shown in Table III below). The average harvested energy is taken between 0.01 µw to 0.16 µw [38]. The simulation settings for all five algorithms are: population size is 20, number of iterations is 500, archive size is 100, and 30 Monte Carlo trials are performed for each case. The extremely large value of this population size (e.g., 90) will increase the computational complexity of the optimization algorithms, which is undesirable. So, an intermediate value of the population is chosen.
To measure the effectiveness of the proposed rank-based multi-objective antlion optimization (RMOALO), we have considered five different test functions F1-F5. The details of the benchmark functional parameters in terms of dimensionality, search domain, and optimal global value are shown in Table IV below [39], [40]. The dimensionality exhibits the dimensions of the test functions, and the search domain marks the test area of the search space, and the global minimum showcases the minimum value taken by the test functions to achieve convergence.
The comparative performance of the proposed algorithm and other algorithms for different test functions is given using the mean minimum, maximum, and standard deviation metrics (see data in Table V).  Rank-based multi-objective optimization (RMOALO) shows the least standard deviation for the functions F1, F2, and F4 and is close to the lowest standard deviation for the rest of the two functions F3 and F5. On the other hand, Multi-objective moth flame optimization and multiobjective particle swarm optimization (MOPSO) have displayed relatively higher standard deviation for most of the functions. This clearly shows that rank-based multiobjective optimization has relatively high stability, thus showing robustness and consistency in its performance. Thus, it can be interpreted that the proposed RMOALO is superior or comparable to other algorithms. For any optimization algorithm, it is very important that it should not be stuck to the local optima and should converge faster.
The convergence characteristics for the benchmark test functions (F1-F5) for each algorithm are shown in Figs. 4-8 for SNR values −15 dB. In this paper, to get a clearer view on the dependency of the fitness function on each variable, the convergence curve is plotted for the optimum value of each variable. The convergence of the proposed algorithm is much better than the other algorithms towards the optimum value of the fitness function. Because of the rank selection method, it is able to successfully overcome the local optima and find the global optima. RMOALO can reach an optimal value in fewer iterations, also avoiding premature convergence.We have evaluated the strength and competence of the proposed RMOALO and other algorithms by applying it to the sensing duration optimization problem to achieve maximum throughput for EHCRN. The fitness function in (11) is optimized for three different values of the harvested energies. Thirty independent runs are made to eliminate any inconsistency, involving 30 Monte Carlo initial trial solutions with a randomly generated population of size 20. The maximum number of iterations is set to 1000. The performance parameters of the formulated problem have been given in terms of the mean, maximum, median, and standard deviation values of the normalized sensing duration (ratio of the sensing duration to the overall time slot) along with the mean fitness value of average throughput (data in Table VI). RMOALO is observed to provide the higher value of throughput in various iterations of the harvested energy Eh at the lowest mean value of the normalized sensing duration. It is also stable in its performance, as it offers the lowest standard deviation among all other algorithms.    The convergence characteristics of the average throughput for different values of the average harvested energy (E h ) are shown in Figs. 9-11. The RMOALO has the ability to overcome local optima with better convergence and is successful in obtaining the best values as compared to other algorithms. The impact of normalized sensing duration on the average throughput with RMOALO reaches a maximum in a few iterations. Thus, RMOALO converges faster to get the higher fitness value.
We can see from Table VI that the behavior of the sensing duration changes with the average harvested energy in three distinct values of the harvested energy E h = 0.13 µw, E h = 0.10 µw, and E h = 0.07 µw. The shorter the sensing duration, the higher the average throughput if the harvested energy is higher. As the normalized sensing duration increases, the average throughput tends to decrease. Therefore, an optimal value of sensing duration 2  exists for the amount of energy harvested for which the average throughput becomes maximum. For a particular sensing time, the average throughput decreases as E h decreases. When E h is maximum, the average throughput R s attains a maximum value, and after reaching a maximum value, it decreases as there is an increase in 2  and decrease in E h .   To validate the effectiveness of the proposed optimization technique, a comparison of throughput maximization for the separated spectrum sensing and energy harvesting (SSSEH) scenario is also done with baseline energy-efficient spectrum sensing schemes in the cognitive radio network. The same initial setup conditions of the sensing duration = 50 µs, average harvested energy E h = 300 J, the sensing energy E s = 1 J, and the energy consumed for transmission E t = 3 J are considered for simulation purposes. Figure 12 shows the analysis for SNR = −28 dB. The throughput achieved using RMOALO shows 14.02 % improvement over the energy-efficient spectrum-sensing schemehomogeneous CR and 6.74 % improvement over the energyefficient spectrum-sensing scheme -heterogeneous CR, as shown in Table VII.

VII. CONCLUSIONS
In the separated spectrum sensing and energy harvesting cognitive radio network with the maximum throughput demands, we maximized the average throughput by optimizing the sensing duration of the ST. This has been achieved by leveraging the proposed RMOALO metaheuristic algorithm. With the SNR value of -15 dB and population size = 20, for varying the sensing time and the average harvested energy, the proposed RMOALO is 16.33 % more efficient than other metaheuristic algorithms considered.
There are several directions in which the analysis of this work could be extended. As the work considers EHCRN and metaheuristics, it can be extended from both realms for some future research, such as non-linear energy harvesting device-to-device network [41], hybrid metaheuristic optimization [42], and bidirectional networks [43].

CONFLICTS OF INTEREST
The authors declare that they have no conflicts of interest.