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1.INTRODUCTIONDue to the ever-growing demand for wireless data transmission, more spectrums are expected to satisfy the future need. However, the scarcity of the spectrum resource poses considerable challenges to spectrum resource allocation and government. To overcome such spectrum shortage problem, the cognitive radio (CR) was introduced to improve the spectrum efficiency by sharing the spectrum resources among multiple users1-3. In general, underlay, overlay and interweave are three different paradigms of CR. They can avail of accessing the spectrum of licensed users simultaneously or the unused spectrum holes opportunistically4-6. While CR is a promising solution for alleviating the spectrum shortage, its intrinsic characteristics raise some new challenges, the most important of which are the quality of service (QoS) provision and the energy efficiency (EE) improvement7. The challenge of QoS provision is originated partly from the dynamic and random nature of the available spectrum. The sharing of the spectrum of multiple users, especially in underlay mode where shared users transmit data simultaneously on the same spectrum band, will not only raise uncertainty to QoS but also deteriorate the EE. Therefore, special consideration should be given to meeting QoS objectives while maintaining high EE within the transmit power restriction. At present, the objectives of most topics on these EE maximization problems are to optimize global energy efficiency (GEE). Although a high GEE can be obtained after the optimization, the EE distribution among the users is obviously different. Some users gain a sensible lower EE performance compared with others8. Recently, deep learning (DL) has received great attention in the area of wireless communication9. Although the DL method used9 can effectively improve SE and EE while reducing time complexity, it is more challenging to obtain label data because the DL methods used are all supervised learning. Unsupervised learning does not require label data, which can further improve the feasibility of the algorithm. An unsupervised learning method to maximize the rate is studied10. Experimental results show that it is superior to existing power control methods. Similarly, the DL method is also used in the fairness of wireless communication11-12. They also used unsupervised learning to obtain max-min SE and max-min EE, respectively, and finally, the proposed algorithm can reach the baseline level. In this paper, a DL-based max-min EE unsupervised learning algorithm in cognitive radio network (CRN) was proposed by us. Expressly, we set SE QoS constraints in PU and SUs, and on this basis, max-min EE. Furthermore, the max-min EE issue under consideration is non-convex as well as challenging to solve. For this reason, a DL-based solution has been proposed by us. A new target function that adds SE constraints to the target term was constructed using our barrier function. The optimized power is output adaptively by inputting CSI. Finally, its effectiveness is verified by simulation. 2.SYSTEM MODEL, PROBLEM DESCRIPTION AND FORMULATION2.1System modelAs shown in Figure 1, CRN-based uplink scenario was taken into account. In this scenario, we consider K base stations and K users sharing spectrum in underlay mode. Among them, the base stations and users are single antennae. A user only communicates with a base station, and other links are the interference link. In the CRN we are considering, the primary network is made up of a primary base station together with a PU, and the secondary network is composed of K -1 SUs with K -1 secondary base stations. We use an instantaneous CSI. yk is defined by us as the received discrete-time baseband signal of the k -th base station, in the meanwhile, its representation can be given as among them, k =1 means PU or primary base station. k = 2,…,K represents SUs or secondary base stations. The channel gain is then defined as hkk for the direct link from the k -th user to the k -th base station. Furthermore, the channel gain hkj of the cross-link is expressed as the channel gain from the j -th user towards the k -th base station. The transmission signal of the k -th user is denoted as xk, the received noise of the k -th base station is denoted as 2.2Problem description and formulationSince the application scenario of this article is a CRN, it is necessary to consider the SE constraints of the PU and the SUs to meet QoS. According to equation (1), the SE for the k -th user could by us then be denoted as Where The ratio of SEk to power consumption Qk is taken as the definition of the EE from the k -th user, which is given by among them, ζ ∈ (0,1] represents the power amplifier factor. Pc represents static power consumption. In this study, the issue of optimizing max-min EE in CRNs is taken into account by us. We try to find the optimal power satisfying the constraint conditions to max-min EE. The problem is defined as among them, i = argmin(EEj), j = 1,2,…,K. The minimum SE constraint from the k -th user is denoted as SEk,min. Pmax denotes the maximum allowed transmitting power for all users. In principle, equation (4) is a nonconvex optimization issue13, where obtaining a globally optimal solution to equation (4) is NP-hard. Some traditional optimization algorithms are limited in their use due to their high complexity14. A DL-based algorithm was developed by us to overcome the shortcomings of traditional global optimization to address the max-min EE issue in CRN. 3.PROPOSED DL-BASED METHOD3.1Problem refactoringIn order to solve the equation (4), we rephrase it as We use the obstacle method as proposed13, and use the SE constraint in (5) as the implicit part of the goal to solve this problem. Specifically, we redefine (5) as15 among them, λ1 and λ2 are the positive control parameters of training. The hyperbolic tangent function is denoted by us as tanh(∙), whose equation expression is 3.2Model designWe use a DNN to solve the equation (6). As shown in Figure 2, we employ multilayer fully connected layers for building the DNN. The input layer of the DNN is K * K dimension H, and the output layer output is a K dimensional P. In addition to the input and output layers, there is an L layers hidden layer, which is located between the input as well as the output layers. We use xl–1 to represent the input of l, where l = 1,2,…,L. Output layer with output node number defined as NL+1. xl can be defined as among them, the weight term, as well as the bias term for the l -th layer from the DNN, are denoted as among them, 3.3Model trainingIn addition, the parameters in the DNN need to be adjusted in such a way that the DNN could learn the relationship between the input and output, and Keras could be employed to automate the gradient descent of the DNN as well as to automatically adjust the parameters. Due to the high complexity of label data acquisition, we use unsupervised learning to build DNN. We redefine the equation (4) to be solved as equation (6), and use a DNN to obtain a sub-optimal solution with less time complexity than traditional methods. In this method, the input CSI of the DNN is According to equation (6), we define the loss function 𝓛(p) of the DNN as We hope max-min EE because the loss value of DNN needs to be constantly reduced and finally converges, so the negative value of max-min EE is adopted. For the QoS constraint, we use the barrier function. When it meets the QoS constraint, the value of this part is 0. When the QoS constraint is not met, this part will produce a more significant positive value. λ1 and λ2 determine which is more important to max-min EE or satisfy the SE constraint. However, when the value of λ1 is much larger than λ2, it may result in the DNN failing to satisfy the SE constraint. Adam was employed by us as a method of gradient descent for DNN. 4.SIMULATION AND EXPERIMENTAL RESULTSThe independent identically distributed complex Gaussian distribution was taken into account as the distribution to which the CSI was generated, i.e. After 1000 iterations, the DNN finally converged. Figure 3 represents the min-EE change curve of DNN under different batch sizes. As seen in Figure 3, the min-EE converges fastest when the batch size is 25, and the slowest when the batch size is 200. Figure 4 shows the min-EE performance of the comparative experiment of different algorithms. As seen in Figure 4, there is not much difference between the min-EE obtained from full power and random power. The min-EE obtained by the algorithm aiming at maximizing the SE and maximizing GEE is not as good as other algorithms, and the min-EE is declining. The min-EE of the DNN algorithm we proposed can finally converge to the same level as PSO16. The min-EE converges to around 0.0719 bps/Hz/Joule. The SE of our proposed algorithm when it finally converges is [0.3015 0.1535 0.3490 0.1994] bit/s/Hz. The SE constraint of our proposed algorithm is finally satisfied. 5.CONCLUSIONThis paper studied the power control method to improve the fairness of EE in the CR interference channel networks, where one PU and multiple SUs share spectrum resources in the underlying model. We propose a fair EE optimization problem that maximizes the minimum EE among all users while satisfying the QoS constraints of the SE. To overcome the difficulty in obtaining the labeled data, we relied on the unsupervised learning strategy when designing the deep learning networks. To train the constructed neural network, we transformed the QoS constraint into a fraction for the loss function through the employment for barrier function approach. The efficiency for the presented algorithm was validated through simulation, indicating that our presented deep learning-based approach achieved similar performance to traditional algorithms. ACKNOWLEDGMENTSThis work was supported in part by the National Natural Science Foundation of China (NSFC) under Grants 61701269, 61832012 and 61771289, the Program for Youth Innovative Research Team in University of Shandong Province under 2019KJN010, the Fundamental Research Enhancement Program of Computer Science and Technology in Qilu University of Technology (Shandong Academy of Sciences) under Grant 2021JC02014,the Talent Cultivation Promotion Program of Computer Science and Technology in Qilu University of Technology (Shandong Academy of Sciences) under Grant 2021PY05001,the Opening Project of Shanghai Trusted Industrial Control Platform under Grant TICPSH202103018-ZC. REFERENCESMitola, J. and Maguire, G. Q.,
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