Power Allocation for OFDMA-Based Cognitive Radio Systems With Joint Overlay and Underlay Spectrum Access Mechanism Using GWFPP and MFO

— Cognitive radio (CR) is a unique idea that allows for more efficient and flexible spectrum utilization. To improve interference control and CR users' total transmission rate, For cognitive radio networks (CRNs), power allocation has been a crucial task. The radio resource allocation problem in Orthogonal-frequency-division multiple access ( OFDMA)-based Cognitive radio networks is investigated in this paper by using the GWF to solve a problem with more severe constraints: (weighted) optimization problem with individual peak power constraints (GWFPP). Unlike the traditional water-filling (CWF) technique, we eliminate the phase of determining the water level by solving a non-linear system based on the target problem's Karush-Kuhn-Tucker criteria. Furthermore, the suggested GWF eliminates difficult derivation in traditional optimization methods, such as derivative or gradient operations, while providing insights into the challenges and specific solutions to the target problems. The outcomes can be enhanced much further when using the MFO technique. The transmission rate improves when GWFPP is used in conjunction with MFO. For a given power budget, the proposed configuration maximizes the total transmission rate of CR users for SUs while keeping interference introduced to primary-user (PU) receivers below stated restrictions. According to numerical results, the proposed strategy is effective, efficient, and simple to implement.


I. INTRODUCTION
Wireless communications networks have grown at an exponential rate, creating new system architecture issues. Without a question, wireless communication is the current and future technology, and the radio spectrum is its most important resource. The radio spectrum's demands are constantly expanding in order to service a broader range of high-data-rate applications.
Providing opportunistic/dynamic spectrum access to a potential user group can increase the use of these underused/unused bands dramatically. These are for users who haven't been assigned to them. Instead, improvements in software-defined radio (SDR) technology [3] have allowed a radio transceiver to undertake baseband processing functions (such as demodulating and modulating using digital, and so on) without requiring any additional hardware.As a result, the SDR became the most efficient method for constructing adaptable transceivers that could connect to a variety of radio networks via a variety of methods. These transceivers must be spectral aware in order to allow for opportunistic spectrum access. As a result, the cognitive radio(CR) technologies designs are influenced. [4].It has been recommended that CR technology be used to improve spectrum use efficiency. This provides unlicensed users with cost-effective access to underutilized/unused spectrums. CR can increase spectrum utilization for an unlicensed customer by bringing underutilized licensed spectrum into operation. Secondary users (SUs) are what they're called [5] [6].
For the next-generation communication network system to function, CR is required. This communication network technology is also known as Dynamic Spectrum Access because it makes better use of the spectrum and does it in a more opportunistic manner (DSA). It does so without generating any problems for the primary users (PUs) OFDM (orthogonal frequency-division multiplexing) has been proposed as a possible air interface technology for CR systems. OFDM is a promising technology in terms of modulation and power regulation. It's also very versatile, because to its reconfigurable subcarrier structure, which allows it to fit into CRNs for optimal spectrum usage.. In addition to its intrinsic benefits, OFDM allows for greater spectrum allocation options. To maintain the interference level required by the PUs, a desirable quantity of power can be provided in different OFDM subcarriers. Also subcarrier configurability allows SUs to fill spectral voids created by PUs in a flexible manner without creating unacceptable interference.
Recently, there has been a lot of interest in power allocation in OFDM/ OFDMA-based CR systems. As a result, the CRN's power allocation is crucial. Using a variety of methodologies, several academics, professionals, and investigators have contributed their work on power distribution. In the last few years, this has resulted in a rush of notable developments in the field of CR.
In [7]the authors investigate a subcarrier and power allocation problem for cognitive radio (CR) systems based on orthogonal-frequency-division multiple access (OFDMA). Rather than looking at resource allocation for either an overlay spectrum access mechanism (OSAM) or an underlay spectrum access mechanism (USAM), this study looked at resource allocation for a joint underlay and overlay spectrum access mechanism (JOUSAM). The total transmission rate of CR users is optimized for a given power budget in a CR system like this, while interference introduced to primary-user (PU) receivers is kept below specific requirements. Because spectrum scarcity is a significant problem, cognitive radio is a viable solution. For cognitive radio networks, orthogonal frequency division multiplexing (OFDM) has the ability to provide various sophisticated functions.
The authors of this [8] work compare and contrast two water filling algorithms: geometric water filling and dynamic channel sensing. This algorithm is designed to maximize the sum rate of secondary users by more efficiently allocating power, while keeping 1) overall transmit power, 2) individual sub channel transmit power, and 3) individual subcarrier peak power of secondary users under control. These algorithms, according to numerical data, make better use of power resources and thereby maximize the sum rate than existing algorithms. Furthermore, the power distribution is ideal. A dynamic power distribution process is geometric water filling. The present state of this process is the difference between the individual peak power sequences and the current power distribution sequence determined by the Algorithm GWF and dynamic channel sensing algorithm The authors of this study [9] investigate the optimal power loading technique for a cognitive radio (CR) system based on OFDM. The downlink transmission capacity of the CR user is thereby maximised, while interference to the primary user (PU) is kept to a minimum. Two less sophisticated suboptimal loading approaches are also presented by the authors. The authors also look into how a subcarrier nulling method affects the performance of the different algorithms. Traditional power loading algorithms used in typical OFDM-based systems, such as water-filling and uniform power but variable rate loading schemes, are compared to the performance of the optimal and suboptimal schemes. The numerical results show that, for a given interference threshold, the proposed ideal system allows CR base stations (BS) to broadcast more power in order to achieve a higher transmission rate than current loading algorithms.
Authors in [10]suggest an iterative partitioned water-filling technique for power distribution in OFDM-based cognitive radio systems . The goal of this method is to maximize capacity while taking into account the per-sub channel power constraints imposed by the PUs' interference limits. Because of the PUs' interference limits, there are power constraints. In real-world systems, the PU is subjected to interference from not just the SU's transmission in the appropriate sub channel, but also side-lobes from other sub channels, which were not taken into account in this research. It is possible to analyze the power allocation problem with additional constraints imposed by surrounding subcarrier side-lobes.
The power distribution approach for OFDM-based Cognitive Radio systems is explored in this [11]. The Geometric Water-Filling (GWF) Peak Power Algorithm is used to suggest a power allocation strategy. For cognitive radio, power distribution is done using a hybrid underlay and overlay spectrum access approach. The proposed technique improves the transmission rate of CR users. Total power and individual peak power limits are taken into account in the suggested method, while the value of interference is kept below a particular threshold value. The transmission rate of CR users has improved significantly. In addition, the performance of the GWF algorithm and an inferior scheme was evaluated.
. For OFDM-based CRNs, this paper [12] presents a subcarrier assignment scheme and a unique power allocation algorithm based on geometric water filling. For a given interference level to the primary users, this algorithm is optimized to maximize the sum rate of secondary users by allocating power more efficiently, while constraining 1) total transmit power, 2) individual sub channel transmit power, and 3) individual subcarrier peak power of secondary users. In comparison to previous methods, numerical results show that this technique makes better use of power resources and hence maximizes the sum rate.
This study [13] proposes simple and elegant geometric water filling (GWF) technique to solve the unweighted and weighted radio resource allocation difficulties. Authors omit the phase of determining the water level, unlike the standard water-filling (CWF) technique, by solving a non-linear system based on the target problem's Karush-Kuhn-Tucker criteria.
The suggested GWF strategy takes less time to compute than the CWF approach with the same memory needs and sorted parameters. In addition, the proposed GWF removes onerous derivation in classic optimization approaches, such as derivative or gradient operations, while also providing insights into the issues and specific solutions to the target problems.. On the other hand, due to the difficulties of solving a non-linear system with numerous non-linear equations and inequalities in multiple dual variables, the CWF is unable to tackle these two general forms of RRA problems. This paper's primary contributions are as follows: The power allocation problem in OFDM-based CRNs is represented by extending the GWF to tackle a problem with both individual subcarrier peak power limitations and is sub-channel power constraints with total power constraints. The proposed method is shown to maximize the sum rate by utilizing power resources more effectively than existing algorithms. The weight factor of each channel also taken into account while allocating power. The power level in different subcarriers using combined GWFPP and MFO has been readjusted, i.e. it is avoided that power distribution is uneven in order to boost the overall transmission rate.
The remainder of this paper is organized as follows: Section II explains the water-filling procedure. Section III introduces the system model and defines the problem, as well as the proposed solutions. The subcarrier and power allocation strategies are explained in Section IV, and RRA Problems Using GWF Approach is detailed in Section V. In part VI, we will simulate utilizing the GWFPP method. Problems with the RRA Making use of GWFPP and MFO Section VII explains how to proceed. Section VIII GWFPP paired with MFO simulation and numerical results analysis Finally, section IX brings the paper to a close.

A. The Conventional Water-Filling (CWF)
In [12], the following describes the CWF problems: the sum signal power is given P T > 0; for the ith channel, allocated power as well as propagation path is described as Pi and hi respectively. Here, i = 1…N; and the total subcarriers are represented by N. If w i >0,Ɐi ,is the weighted N will be monotonically and positively decreasing , so the optimization problem can be written as: The power allocation strategies for spectrum resources will be very flexible and convenient when implementing Orthogonal Frequency Division Multiplexing in cognitive radio networks [7]. However, in OFDM-based cognitive radio networks, allocating power to particular sub-channels becomes extremely difficult. Water-filling algorithms are common in classical power allocation problems. Water-filling methods are always used iteratively to solve the power allocation problem in cognitive radio networks since additional interference constraints must be considered C1 is the nonnegative allocated power, and C2 is the overall power constraints in the equations above. The KKT conditions, which are regarded as a group of optimality conditions , are commonly utilized at the beginning for finding the solution of the problem (1). KKT conditions are significant conditions for optimization and are regarded sufficient if the problem is convex. However, in order to allow for the unified and effective water-filling algorithms, the generated water-filling solutions may not have a systematic and compact format. The water level (µ) is chosen for satisfying the power sum restrictions with equality in order to obtain the best solution. ∑ = =1

B. Geometric Water-Filling (GWF) Approach
To tackle the standard water-filling problem and its weighted counterpart, a geometric waterfilling (GWF) approach is proposed in this chapter. It has two benefits. On the one hand, the geometric approach can compute the exact solution to the CWF, including the weighted case, with less computation and easier analysis than solving the non-linear equation system. On the other hand, the proposed geometric technique can overcome the CWF algorithm's limitations by incorporating more strict constraints. Unlike the CWF algorithm, it eliminates the steps to identify the water level. Under the same memory need and sorted parameters, the GWF algorithm requires less processing than the CWF technique.
We expand the proposed GWF to tackle more generalized individual peak power constraints (WFPP) problems by using the notion of water-filling and the provided geometric machinery.
In this work, we present a novel geometric technique to solving the problem (1). The proposed Geometric Water-Filling (GWF) approach eliminates the procedure for solving the nonlinear system for the water level and instead provides explicit solutions as well as useful insights into the problem and solution. The suggested GWF algorithm is depicted in Figure1. In a water tank, suppose there are four steps/stairs (K = 4) of equal width. The dashed horizontal line, which represents the water level, must first be found, and then the power assigned for each step (water volume above the stair) must be solved. Rather than attempting to find the water level, which is a real nonnegative number, we strive to determine the highest step beneath water, which is an integer value ranging from 1 to K, denoted by k. We can immediately write out the solutions for power allocation based on the outcome of k.
Figure1: Illustration of the concept of water filling algorithm

C. Weighted Water-Filling With Individual Peak Power Constraints
In [12],the CWF problem and its weighted form are solved with the help of GWF approach. The highest water level step which is denoted by k* is introduced instead of trying to analyze the water level n, for finding the power allocation solution.
Let the water volume above step nor zero is denoted by the Pt(n), whichever is greater and the value of Pt(n) can be found by ]} + , for n = 1, … N Here, ith stair is the depth of the stair denoted by 1/hi and the difference of step depth is denoted by the (δ n,i ) for the ith as well as nth stair. Due to the definition of Pt(n) being the power (water volume) above step n, it can not 0 to Pi(n) is the result inside the bracket is negative, the corresponding geometry meaning is that the nth level is above water. According to [13], the explicit solution to (1) is: Where, the water level step n * is given as n * = max{n P t (n) > 0,1 ≤ ≤ } and the power level for this step is

III. SYSTEM MODEL AND PROBLEM FORMULATION
A contiguous chunk of radio spectrum with total bandwidth W is available in a specific geographical area We analyze a downlink transmission situation in which a CR transmitter dynamically transmits data to K CR users across the entire spectrum of bandwidth W. The multiple-access mechanism in the CR system is OFDMA, which divides the entire spectrum into Z subcarriers with spectral spacing between two adjacent subcarriers, i.e., f = W/Z. In the CR system, there is a spectrum sensing mechanism that can be used to determine whether a specific subcarrier belongs in the bands that are available. Whether or whether the PUs are now occupying the space. We suppose that there are N overlay subcarriers and L underlay subcarriers at any one time, and that N + L = Z. In the spectrum domain, one conceivable cohabitation scenario of PUs and CR users with the JOUSAM is presented in Fig.3.3. The majority of the previous work centered on building power-allocation and/or subcarrier-allocation algorithms using the USAM or the OSAM. To maximize total spectrum utilization, CR systems may need to exploit not only the unused bands in a given geographical region at a given moment, but also the surrounding underutilized bands

A. Modeling of PU Interference and CR User Capacity
The power spectral density φ k (f) of the kth subcarrier can be expressed as [5] ( ) = 2 ( ) .
Where T s is the symbol duration and p k is the power loaded in the kth subcarrier. The spectral distance factor ( , ) is defined as [9] ( , ) = ∫ 2 ( ) , +Δf/2 , −Δf/2 (9) Where, d k,l represents the spectral distance between the kth CR subcarrier (i.e., the overlay subcarrier) and the lth PU subcarrier (i.e., underlay subcarrier). Let h l SP is fading coefficient of the channel between CR transmitter and lth PU subcarrier. The interference created by CR subcarrier to lth primary user group can be given as [5][6] Where ρ u,k denotes the status (0 or 1) that k th subcarrier is allotted to the u th CR user.

B. Problem Formulation and Objective Function
For a given total instantaneous transmission power budget and values of h u,k SS the design goal is to optimize the total transmission rate of K CR users while keeping the total instantaneous interference to the underlay subcarriers below a threshold. In other words, the interference introduced to the lth underlay subcarrier can be assured to stay below a specific interference threshold I th l with a given probability a. The problem can be expressed mathematically as an optimization problem as follows for all u and k The power among CR users, efficient allocation of sub-carriers, and exponential complexity based on input size describe the combinatorial optimization issue. As a result, the problem will be solved in two parts using several suboptimal algorithms: first, the subcarriers will be allotted to the CR users. Second, power distribution for these subcarriers.

A. Subcarrier Allocation
We assign a subcarrier to a CR user with the highest signal-to-interference-plus-noise ratio for that subcarrier, because the goal in (5) is to optimize the total transmission rate.

B. Power Allocation
One of the most significant resources is the transmit power that efficiently concludes the system's reliability and rate. The optimization for attaining the system's required performances can be achieved by cautiously assigning authority to the transmitter for every subcarrier, and it depends on its quality. This design aims to maximize CR users' total transmission rate along with keeping the sudden overall interferences of the underlay's subcarriers under the thresholds for a provided overall sudden power budget for the transmission. This is made over the provided values of h u,k SS . The resource assigning target maximizes the CR system's downlinks overall capacity below the general power constraints and the total interferences constraints. Thus, the mathematical expression for this issue can be stated as below:

and ∈ Ω
The issue of allocating the problem in the CR system can't be sorted quickly through utilizing the conventional WF technology as extra interferences constraint must be brought under consideration in the CRN. Constraint C1 considers constraints of peak power of the individual, C2 comprises of the overall conditions of the power, and C3 comprises the power constraints of the sub-channels that occurred because of the interference's limits of the primary users. In the research [37], the introduction of C1 was made and the researchers presented methods for solving the weighted RRA issues and optimal outcomes. This chapter is created by combining C1 and C2 for constructing an optimal scheme for assigning power.

V. SOLVING GENERALIZED RRA PROBLEMS USING GWF APPROACH
An assumption has been made for the practical implementations that gain of the channel h l SP The transmitter and receiver of the CR and PU, respectively, are not acknowledged at the transmitter of the CR. But the h l SP statistics are well-known at the transmitter of the CR. It is assumed that every subcarrier goes below the flat fading's of the frequencies, and the sudden gains in this fading are flawlessly known at the transmitters.
Every underlay subcarrier in this investigation received the same amount of power. However, the power allocation for the overlay subcarrier is done using the ladder profile described in [9]. The ladder profile is created using the heuristic. For the PU bands, subcarriers present larger interferences, hence their allocation should be made with a lower power. The underlay's subcarriers' power profile (that is assigned with the exact amounts of energy) may be expressed: It is proposed through this work for allocating the P OV power to the subcarriers of the overlay, which is nearest to a band of the primary users. After that, it is proposed to allocate the Pov power to the next nearest subcarriers of overlays. Mathematical expression for the overlays subcarrier's power profile will be: This work proposes assigning P OV power to the overlay subcarriers closest to a band of principal users. Following that, it is proposed that the POV power be allocated to the overlays' next closest subcarriers.
Δn signifies the spectral distances among the nearest Primary user's band and overlay subcarrier nth

VI .SIMULATION AND NUMERICAL RESULTS ANALYSIS USING GWFPP
This section contains a simulation for this optimization as well as the GWFPP algorithm (shown in figure3) that was employed.

Figure Fehler! Kein Text mit angegebener Formatvorlage im Dokument.: GWF algorithm
Furthermore, in the given power allocation problem, the constraint of total power budget and individual subcarrier peak power are considered for OFDM-based CRNs. This simulation of OFDM-based CRNs is performed using MATLAB language. The system parameters for the simulation are given in table1.  figure 3.5.
Figure4: Typical attenuation level for different subcarriers and different channels.
In figure 4, attenuations of different CR users are shown by a different color. For this channel, the power budgets are used in simulation in the range of .1 mW to 9 mW. The simulation to optimize the transmission rate by optimizing subcarrier power allocation has been carried out for different total power budgets and interference levels.
During the simulation, multiple power budgets were utilized, and the transmission rate achieved at I=500 was compared to the suboptimal method of optimization [7]. A further effect of the allowable interference level on the transmission rate is investigated at various power budget levels.   For each value of the interference constant(I), the result has been analyzed. Furthermore, in the presence of an interference level threshold, the maximum permissible total power budget for various channel conditions was determined. Table 2 summarizes the findings. The maximum allowable total power increases with greater attenuation for a particular interference, as shown in the table above. An rise in the interference threshold, on the other hand, allows for the use of higher transmission power and hence a higher transmission rate.. The maximum achievable transmission rate for the above simulation is shown in the table 3

VII. SOLVING GENERALIZED RRA PROBLEMS USING GWFPP AND MFO APPROACH
Using combined GWFPP and MFO power level in different subcarrier has been readjusted i.e. it is avoided that power allocation should not be uneven so as to increase the overall transmission rate . In this process no subcarrier has been allotted power level up to peak power level. Based on the moth's transverse orientation towards space, MFO algorithm inspired by nature has been developed. Transverse orientation uses a fixed angle through the moon for flying in straight directions at night for navigation. With local search techniques, the MFO combines algorithms based on populations to produce an algorithm that can both explore globally and exploit locally. MFO is simple to incorporate, adaptable, and straightforward, and it shares a lot of similarities with Metaheuristics MFO can also be used to solve a wide range of problems. With these benefits in mind, MFO was successfully implemented to solve a variety of difficulties. Image processing, energy, power, economics, categorization, estimating parameters, and so on are some of the applications that can be presented. [14].
Using the JOUSAM model, we devised and implemented a system as shown in figure8, to optimize power, which resulted in an increase in transmission rate.

VIII. SIMULATION AND NUMERICAL RESULTS ANALYSIS USING GWFPP COUPLED WITH MFO
The optimization result of GWFPP coupled with MFO is likewise analyzed for the same CRN structure, just as it is for GWFPP-based optimization. Table 1 lists the system settings for the simulation for the sake of competition: The average attenuation of Rayleigh fading, which was utilized to assess the GWFPP's performance, is roughly 80 to 90 dB. This simulation also uses power budgets ranging from.1 mw to 9 mw for this channel. In this simulation, MFO is used to determine the ideal peak power for each subcarrier, and then simulations for various channel attenuation levels[80 dB, 83 dB, 86 dB, 89 dB].
. In presence of an interference level threshold, maximum allowed total power budget were identified for different channel conditions. Results are summarized in table 5 The maximum achievable transmission rate for above simulation is shown in table 6.  The figure below shows a Transmission rate improvement with average channel attenuation and interference constant clear improvement of ~ 2%.

IX. CONCLUSION
The maximum transmission rate achieved during simulation 14.3 Mbps, which is the most efficient transmission rate than the transmission rate of 12.9 Mbps without GWFPP based optimization. During optimization, the peak power of each subcarrier has been maintained, and assigned power is kept below the respective peak power. One intriguing finding can be deduced from the table3. Because of the increased channel attenuation, we can take use of higher transmitted power. This is translated into a higher transmission rate. In general, the opposite is Channel attenuation =89 dB true. This is due to an increase in the maximum allowable power as well as interference limitations. From the table5, it can be observed that for given interference, Maximum allowed total power is same as in the case of GWFPP based optimization. The maximum achievable transmission rate for above simulation is shown in table 6. These results show a significant improvement in the GWFPP and MFO when compared to simply GWFPP-based optimization. The graph below demonstrates a significant improvement of 2%. Figure 10 shows the improvement in transmission rate. With the proposed technique, an improvement of 1 to 2% was realized in each case. It was possible to obtain a maximum transmission rate of 14.71Mbps.