# A Deep Learning-Based Power Control and Consensus Performance of Spectrum Sharing in the CR Network

Authors: Muhammad Muzamil Aslam; Liping Du; Zahoor Ahmed; Muhammad Nauman Irshad; Hassan Azeem
Journal: Wireless Communications and Mobile Computing
 (2021)

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## Abstract

The cognitive radio network (CRN) is aimed at strengthening the system through learning and adjusting by observing and measuring the available resources. Due to spectrum sensing capability in CRN, it should be feasible and fast. The capability to observe and reconfigure is the key feature of CRN, while current machine learning techniques work great when incorporated with system adaption algorithms. This paper describes the consensus performance and power control of spectrum sharing in CRN. (1) CRN users are considered noncooperative users such that the power control policy of a primary user (PU) is predefined keeping the secondary user (SU) unaware of PU’s power control policy. For a more efficient spectrum sharing performance, a deep learning power control strategy has been developed. This algorithm is based on the received signal strength at CRN nodes. (2) An agent-based approach is introduced for the CR user’s consensus performance. (3) All agents reached their steady-state value after nearly 100 seconds. However, the settling time is large. Sensing delay of 0.4 second inside whole operation is identical. The assumed method is enough for the representation of large-scale sensing delay in the CR network.


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## Body

## 1. Introduction

Intelligent processing is one of the major advantages of CRN [1]. Due to this feature, these systems possess the capability to learn their environment, increase awareness, and reconfigure themselves accordingly. High environmental awareness of these systems, due to their ability to perceive, gives them an enormous advantage in a wireless communication environment. Therefore, a device’s wireless operations can be effectively adapted to its surroundings, and thus, it uses the maximum resource to deliver the best results. Some techniques, e.g., intelligent reflecting surface (IRS), for secure communication of multiantenna have been studied in [2] which contain reflector elements that are reconfigurable and controlled by software that is communication-oriented [3, 4]. In most cases, spectrum sensing is used to achieve perception capability in these systems [5]. Therefore, weak spectrum sensing ability would limit their operations and, as a result, decrease the efficiency. In this context, many researchers have proposed techniques to improve spectrum sensing [6, 7], which contain, but are not limited to, wideband spectrum sensing, cooperative spectrum sensing [8], and sequential spectrum sensing. It is a concept widely used for perception improvement in a wireless networking environment [9]. In this context, spectrum measurements, multidimensional spectrum sensing, and interference sensing [10] have been studied extensively.Primary users’ (PU) role is considered an active and passive user model in academia for spectrum sharing. There was a cooperative or noncooperative relationship between PU and SU in the active models [11]. To enhance the transmission performance of the system, information interaction has been performed, although, in research, SU performs spectrum sensing in a passive user model for finding power allocation or idle spectrum. When there is a passive PU role, then PU assigns its transmit power relying on its power controlling scheme [12].CRN transmit power selection must be properly controlled for the transmissions of the CR users [13, 14]. This is the factor that can help to achieve high efficiency of the spectrum through reuse of the spectrum bands of the power units which are affected by the PU limitations. For spectrum sensing, resources are required at all nodes [15]. Hence, effective development of spectrum sensing is of high significance to achieve optimal bandwidth, time, and power spent in between the transmission and sensing [16–18]. Intelligent [19] wireless communication devices must be adaptive to their environment to be able to perceive their surroundings. This can be achieved through the optimization of working limitations and dynamic spectrum access.In recent years, fast developments in machine learning have been noted. Applied in different problems of wireless communication [20], both supervised and unsupervised learning [21] have been considered. Different from supervised learning, Q-learning or reinforcement learning [22] is found to be valuable to maximize the long-term performance of a system and to achieve a balance between exploitation and exploration. Furthermore, deep learning has proven to be a predominant method of achieving sound and higher performance, which is unaffected by massive data sets, and also seems promising in wireless communication [22]. In this context, reinforcement learning is a machine learning technique inspired by biological phenomena, where knowledge is acquired to an agent by repeated trial-and-error communication with its surroundings. Environment feedback to an agent’s action is used to optimize the machine for future behaviour. Dynamic interaction between the agent and its surroundings and the resulting response are two of the key topographies which make reinforcement learning techniques appealing for cognitive radio ad hoc network applications, mostly for the tasks of routing and spectrum decision [23]. In several cases, operations based on reinforcement learning are better than traditional solutions [24].For better performance of CRN, awareness about surroundings (radiofrequency (RF)) is a must for CR. CR should sense and check all around the location for keeping an eye on the RF activities. There was a basic identification of spectrum sensing in CRs. Some sensing techniques, e.g., energy detection, based on a matched filter and cyclostationary process, have been studied in [25]. For better results of sensing accuracy, cooperative sensing was studied in [26] to focus on wireless network hidden terminal problems. Recently researchers studied cooperative CRS [27].Cooperative communication is an advanced communication-in-future technology that optimizes signal transmissions w.r.t both medium contact control and physical coating as presented in [28]. There is an important role of Q-learning in CR application, for instance, dynamic spectrum access. Users iteratively improve their planning to attain their tasks through knowledge and recompense from their surroundings. In these days, there are several research techniques to solve the problems of power control and power allocation [29], for example, game theory [30], optimization theory [31], and machine learning; among these, deep reinforcement learning which is a kind of machine learning has got a lot of attention because of its fast speed over the complex problem. The contribution of its challenging ability in many applications can be found such as Atari Games [32]. Agents [15] that are trained through reinforcement learning are intelligent enough to absorb their act value policies from high-dimensional rare data. An example of such applications would be videos or images [33] also shown in our tentative result.Deep ReLU (rectified linear unit) learning can assist in learning an operative action charge policy even when the state notes are contaminated by measurement errors or arbitrary noise. Using deep reinforcement learning power control-based spectrum sharing in wireless networks showing the relation between PU and SU, wireless sensors have been studied in [34] and channel selection policy for PU and SU has been studied in [35]. On the other hand, the conventional ReLU method is unfeasible for such issues because of an inadequate number of states in the presence of arbitrary noise. Therefore, deep reinforcement learning is appropriate for wireless communication applications, where municipal dimensions are usually arbitrary. In this paper, we described the consensus performance [4, 36] and the power control of spectrum sharing in CRN. We also introduced a sensing delay. In CR, power control is investigated for spectrum sharing to assure the quality of service for PU and SU. First of all, CRN users are considered noncooperative users such that the power control policy of primary users (PUs) is predefined, while the secondary user (SU) is unaware of PU’s power control policy. Secondly, a model was constructed for cooperation between wireless sensors, PU, and SU. In this model, wireless sensors’ received signal strength is spatially distributed to assist PU for power transmission information with SU. The performance criterion of sharing in CRN has been improved in the presence of sensing delay in a communication network. The studied model can get minibatch updates for several iterations. The network becomes able to converge quickly and meet a user’s quality of services. The overall contributions of this work or difference with other works can be summarized as follows:
(i)
The proposed method is different from the traditional method in the sense that there is a performance criterion of sharing, and consensus of CRN has been improved in the presence of sensing delay (communication delay) through the communication topology(ii)
An agent-based approach is introduced for the CR user’s consensus performance for the first time(iii)
Besides, a deep learning power control strategy (reinforcement learning) has been developed along with an agent-based approach altogether for a more efficient performance of sharing controlIn the rest of the paper, we discussed the following: overview of CRN, intelligent power control of spectrum sharing, delay performance using a primary sensor network, and CRN consensus criteria under communication delay.


## 2. An Overview of CRN

We suppose a CRN which contains licensed users and unlicensed users; in this, the unlicensed user is willing to segment spectrum resources which are common with the licensed user, without any danger to harm the licensed user activity. The licensed user contains the primary transmitter (PT1) and receiver PR1; similarly, the unlicensed user consists of a secondary transmitter ST2 and receiver SR2. The receiver and transmitter of both licensed and unlicensed users are shown in Figure 1 in a multicluster network number of sensors that are present for direct communication with the central station; the central station can be the Cluster Head (CH), the name cluster is because of network similarity with neural network. In our supposed work, there is no working cooperation between the licensed and unlicensed users, where a licensed user does not know the presence of the unlicensed user in the same surroundings even licensed users adjust its conduct power built on its particular power policy. The next step of the licensed user will be affected in a couched way by the sudden action of the unlicensed user; it should be highlighted that for the licensed user, the power control policy depends on the network of licensed users and the number of sensors used. Yet licensed and unlicensed users are without communication, and both have no information about the power transmitter and power control policy of each other. For an easy understanding, we consider that licensed and unlicensed users synchronously update their transmit power, where it is based on the time frame base.Figure 1
Spectrum sharing in CRNs (sharing the same channel).Here, in terms ofSNRc, it is used for showing the quality of the system of licensed and unlicensed users. ∂a and ∂b show the transmit power of licensed and unlicensed users. The receiver value of SNRc is given as
(1)SNRc=Hxx2∂a∑y≠xHyx2∂b+Nx,∀x=1,2.In Equation (1), Hxy is the frequency expansion from PT1 (primary transmitter) to ST2 (secondary transmitter), while Nx is the noise power from PR1 (primary receiver). Here, the purpose is to assist the unlicensed users in acquiring sufficient control power policy, so that after some time of power adjustment, both licensed and unlicensed users are intelligent for the successful transmission of data with the essential quality of services. If unlicensed or licensed users are only aware of their transmit power, then such a task is complicated. To assist unlicensed users, in a wireless communication network using different locations, sensor nodes are hired for the dimension of received signal strength (RSS). Received signal strength measurements are related to both (licensed and unlicensed) users’ transmit power, close-fitting the information system from the state. Here, we suppose that RSS information is helpful for the unlicensed user. Zigbee technology [7] and CRNs generally function with different frequencies, and there is no interference in transmission because of sensor node transmission in CRNs. Tocollect the received signal strength information from spatially scattered sensors, node is a basic condition, for example, source localization [17]. In the proposednumerical method, only once per time frame is needed to report RSS informationwhichconsists of low data rate.We considerPR1 and SR2; here, SR2 mollify the lowest SNRc aimed at an effective response. For getting the quality of system condition, the licensed operator or user is considered to deceptively regulate its power transmission that is power control policy-based. We used “2” controlling power policies that supposed for licensed users, even if the licensed user (PU) adopts any other power control policy, our supposed method will also work. For the first policy, the transmit power of the licensed user is updated following the classical power control algorithm. Transmit power is adjusted on a time framed bases K(x) that maps the continuous values level, known as discretization operation.
(2)∂ar+1=Kω′c∂arSNRcr.Here,SNRcr is the SNRc measured at PR1 at the rth time frame. ∂ar is the transmit power at the rth time frame.Now, we explain the PU policy of our supposed work. Let us see(3)∂ar+1=∂y+1∂,if∂y∂≤η∼≤∂y+1∂andy+1≤E1,∂y−1∂,elseη∼≤∂y−1∂andy−1>1,∂y∂,otherwise,Here,ῆ∶=ὡc∂ak/SNRcr; compared with Equation (2), Equation (3) has more unadventurous behaviour for power control policy. Transmit power is updated step by step. The power is increased by a single step when SNRcr≤ὡc and ὡ≥ὡc; also, the power is reduced by a single phase, when SNRcr≥ὡc and ὡ≥ὡc. If not increasing or decreasing, then it will stay at the present power level. And here, ὡ∶=SNRcr∂ar+1/∂ar is the forecast SNR at the (r+1) time frame. Now,
(4)P1≈∂a∂⋯∂E1∂.Here,∂aԺ≤⋯∂. Furthermore, precisely we suppose that Kx is very equal to a discrete step, which is not lesser than x, and suppose that kx=∂ if x>∂. Now, assume the second power control policy and consider that the transmit power at the rth time frame is ∂ar=∂yԺ, where ∂yԺ∈P. Equation (3) shows the transmit power of PUs updating.A suggested control channel is used to notify the sensors about the available users. Scheming a CRN without a suggested control user can be studied in [9]. Sensor node switch between various users depends upon the available user; also, there is a possibility of the sensor to operate on different users. Further info about this can be found in [30]. A multiradio wireless sensor network has been explained in some literature which can be found in [18]. In this research article, consider that N sensors are installed to sample the received signal strength info. Consider that Ṣn represents node n and ∂nmr represents the receiving power at the rth frame at sensor n. We simulate the state of received signal strength observations.And now, the SU policy is explained in the form of the following equation:(5)∂nmr=∂arJcn+∂brJdn+Lnr.In Equation (5), ∂ar represents the transmit power of PUs, ∂br represents the transmit power of SUs, Jcn is the path loss between sensor n and the primary transmitter, Jdn is the path loss between the unlicensed transmitter and sensor n, and Lnr is the zero mean Gaussian random variables with variance φn2.Here, according to free-space broadcast, with regard to the Friis law,Jcn and Jdn are given below:
(6)Jcn=γ4πD1n2,Jdn=γ4πD2n2.Usually, the Friis equation is used for the calculation of ideal power which was received at an antenna from elementary info about the transmission. Here, “Ɣ” is the wavelength of the signal D1n and D2n showing detachment between nodes and primary and secondary transmitters. The Friis equation is used only for the calculation of single frequency, even though transmission characteristically contained many. Here, also to suppose, from a finite set, we choose the transmit power of the unlicensed user:
(7)P2≔∂am⋯∂E2m,where ∂am≤⋯≤∂E2m; the SU goal is to see how power transmission can be settled depending on the received signal strength info ∂nmrn; after rare rounds of power transmission at every time frame, both PU and SU can see their respective quality of system necessities. At least transmit power is present in our supposed work, which transmits power ∂s1Ժ,∂s2m; here, PR1 and SR2 mollify their quality of system SNR necessities.


### 2.1. Intelligent Power Control of Spectrum Sharing

The distribution of system time is uniform, denoted as channel switching intermission. The presently employed channel develops unattainable culmination of the cooperative spectrum interval. When the sensor senses the second user, the channel might delay till the start of the next cooperative spectrum pause (if at least one user is available). In that case, both the user and sensor jump to the new channel. This process is termed as periodic switching (PS). Another cause may be that the central head may highlight the sensor if a new channel is available, as the prior channel is misplaced; this channel loss is stated as triggered switching (TS). The number of channel switching may be zero or one for periodic switching (PS); it depends whether the channel is present or not at the start of the cooperative spectrum interval. For a satisfactory transmission, the central station sends back an Automatic Control Key (ACK) to the sensors. If the sensor does not receive an ACK after a data packet transmission, it is assumed that the present channel is unavailable, and the transmission is stopped immediately. However, this kind of failure may happen due to channel fading which would cause a transmission failure on the CR sensor net. It is not a good practice to stop the transmission in this case, which would instigate needless interference with the PN (Primary Network). Therefore, BE (Best-Effort) data traffic and actual-time data traffic can be assisted in this case. A good example of this channel switching and traffic resource allocation can be found in [2].In the proposed work, SUs are assumed to take any action at each time step, such as for choosing transmit power from the earliest quantified power setP2 based on its present state. To analyse this, the Markov decision process (MDP) [37] is considered. Particularly, for instance, consider an action är=∂r+1 by SU in the state mr. Then, the next new state mr+1 is dependent on the present state mr and action of a decision-maker är. Here, mr and är are known. The following states will be independent of all earlier states and actions with the condition that
(8)mk≈∂an∨r⋯∂Nn∨rT.For a new state, a corresponding rewardňr∶=ňmr is assumed for the decision-maker är which can be mathematically expressed as
(9)n∨r≈z,ifSNRcr+1≥SNRdr+1≥ω′d,0,otherwise.In this work, “z” is assumed to be 10. It can be seen through simulation that the value of z should be sufficiently large to avoid the learning disturbance. Communication between a SU, a PU, and the sensors is shown in Figure 2(a). It is to be highlighted that the unlicensed user is supposed to distinguish whether communication between PT1 and PR1 is successful or not. This kind of information can be gained to monitor an acknowledged signal transferred PR1 for an indication of successful transmission from PT1. Figure 2(b) [15] shows the detached control architecture and is an object control system design in which there is a linear time-invariant (LTI) and multiple input-multiple output (MIMO) system.Figure 2
Unlicensed user and licensed network interactions and standard multiuser close loop.
(a)
Primary/licensed network
(b)
Standard multiuser close loopThe basic problem for the Markov decision process is to understand the policy for the decision-maker.(10)Uπmr≔∑a=rT−1γa−rn∨a,where π stipulates the action πm from the decision-maker. It is important to say that the purpose of SU is to understand a strategy π for the selection of its action är which is constructed on the present state mr in a method that discounted cumulative reward reduced maximum as studied in [38]. In Equation (10), “Ɣ” is the discount factor and T−1 is representing the time frame, at which the targeted state is touched. In this case, the targeted state is well defined, where SNRcr≥ὡi for i=1,2. The target is for studying optimal policy π∗ that maximizes Uπ, i.e.,
(11)π∗=argmaxUπm,∀m,It is complicated to directly learnπ∗. In the case of reinforcement learning, there is an alternative approach to solve Equation (11) through Q-learning. This alternative approach has been studied in [13]. Q-function (action value) is defined to determine the predictable reduced growing reward after the action ak+n, for state m. In such cases, the optimal policy would be built by choosing the action by the largest value in each state.By the updated Bellman equation,(12)Qm,a=n∨m,a+γmaxQm′,a′mThe elementary purpose ofQ-learning and several other reinforcement learning algorithms is to iteratively update the action value according to the value updating instruction. In Equation (12), “m′” is the state followed by smearing of action “a” to the present state “m.” The value iteration algorithm defined in Equation (12) approaches the best action value purpose. The number of states is limited for Q-learning, and at each state, the action value function is guessed separately. The Q-table is designed such that rows represent the states and columns represent the probable action state. One can choose an action from the Q-table as the maximum value of Qm,a through an optimal action state. However, the value of state function m is continuous due to arbitrary variation in the received signal. Therefore, the Q-learning method is unfeasible in this work since it is not convenient to consider an unlimited figure of states. To overcome this issue, DQN (Deep Q-Network) is opted. A brief study and proposed work of DQN are presented in [39].Different from the traditionalQ-learning technique, which is used to generate unlimited action value functions, “ϑ” is used here to express weights of Q-learning, while the Q-table is substituted by the deep neural network Qm,a:ϑ that would act as the action value function. Particularly, for an input “m,” DQN produces an E2-dimensional vector for selecting action a=Ժim from p2. When mr is given, the data used for Q-network training is generated as follows: we explore amorphous selected action with ϵk having the largest output Qmr,ar:ϑ0, where ϑ0 is used for denotation of the present iteration. Subsequently, the action an (r), SU gets a reward ϒ(r), a new statemr+1is obtained. This transit, dr∶=mr,ar,mr,mr+1, is held in the reiteration memory K. When enough transitions are collected in K, the training of the Q-network begins. Say O=300 evolutions, we casually choose a minibatch of transitions dii∈Ωr from K, and with adjustment of ϑ, DQN can be trained as given loss function is minimized:
(13)Eϑ≈1Ωr∑iε℧rQ′i−Qmi,a⋯i;ϑ2m.Ω
r is the index set of the irregular minibatch used at the rth iteration. The estimated value of the Bellman equation Q′i for the ith iteration is given by
(14)Q′i=n∨i+γmaxQsi+1,a..;ϑ0,∀iεΩrm.Different from the conventional supervised learning, the goal for DQN knowledge is different from that of the traditional approach.SU can select action after training, which gives a maximum projected valueQm,ä,ϑ∗. For simplicity, the DQN scheme is summarized in the power control scheme for SU. It would be clearer to highlight that during the training process of DQN, an SU needs the knowledge that satisfies the QoS (quality-of-service) necessities for the PU, and therefore, the SU is mollified. However, the only purpose of SU, after DQN training completion, is feedback from the sensors for the decision of the next transmit power. The junction problem of the supposed policy for power control is hence studied. Let “m” be a target state; then, if SU transmit power stays unchanged, it will be informal to say that the next state m′ is also a goalmouth state. Transmit power can result from either Equation (2) or (3), and as a result, PU will be updated. In another way, SU will ultimately acquire to select a diffuse power as m′ persists the goalmouth state. It can be concluded that once s achieves the target state, it will be in the goalmouth state till broadcast information is done. Now assume that there is a possibility of data loss because of the irregularity of data transmission and SU aims to take up for an innovative transmission; no long learning is required in this case. Rendering to control power policy, SU can select transmit power.Figure2(b) shows a standard multiuser closed loop representing power control in this case. Standard discrete time is considered for control system design. For a multi-input multioutput system called the MIMO system with linear time-invariant known as LTI, there are z input, w inputs, and h states.
(15)Zq+1=XAl+Qvl+Wlm,Cq=KAq+Hqz,where “q” represents the time index linked with T time sampling in the discrete time domain. X∈,K∈Ȑz∗n and Ȑn∗n,Q∈Ȑn∗m are output matrices and system input, and W. and H. are system measurements and disturbances, respectively. U.=u1.,⋯,uf.T and Y.=y1.,⋯,yz.T are expected to be barred, for example, ∣ui.∣≤giu,i=1,⋯,f and ∣yj.∣≤gjv,j=1,⋯,z, in which giu’s and gjv‘s are positive constant. For simplicity, all states are considered measurable, i.e., K=I. There is a possibility to design a feedback controller at state (1) through maximum input maximum output, which is shown as follows.
(16)VM=Mkqm,MMq−AC+Hqm.Algorithm 1: Power control policy-deep learning training based.
Initialize D with capacity O
Initialize networkQm,a,ϑ with variable weights ϑ=ϑ0
InitializeԺa and Ժb and then obtain m (1)
Forr=1, r do
UpdateԺar+1 via power control policy of PU (2) or (3)
With iterationsεk, choose an arbitrary action ak; otherwise, select ak=maxaQmr,a;ϑ0
Obtainmr+1 via arbitrary model (5) and detect reward nr
Store transitiondr∶=mr,ar,mr,mr+1, in D
Sensing delay
Repeat sensing delay
Ifr≥O then
Sample random minibatch of iterations fromDdii∈Ωr,
Here, theΩr index is uniformly selected at independent
Minimize loss function of 12, in which goal is given by (15) Q′i
Adjustϑ0=argminϑEϑ
End if
mr is the target state and then initialize ∂ar+1 and ∂br+1 and then gain mr+1
end if
end forThat is, Figure3(b) shows the spectrum sharing of the control system, which is well designed. So, the stability and performance of the system (z) could be definite through an approximate selection of V sampling time in Equation (16) and K as gain feedback design in Equation (15). A dynamic system is to be supposed (Equation (15)), there is a designed controller that works as a designed framework baseline.Figure 3
Sensing delay (sensing time) and spectrum sharing between users.
(a)
Sensing time delay
(b)
Spectrum between usersIn this paper, there is a consideration that the PU and SU update their power of transmission synchronously. However, we would like to highlight that our proposed scheme’s synchronous assumption is not a must. Consider that there is no strict synchronous occurrence in the time frame between PU and SU; both synchronize transmit power at the start of a timeframe. Figure4 represents the transmit power of a licensed and unlicensed user. PU adjusts its transmit power at time ʈp,ʈp+T,ʈp+2T⋯, whereas SU’s transmit power is updated at ʈs,ʈs+T,ʈs+2T⋯, where T is representing the time of each setting. Deprived of loss simplification, we consider thatT>ʈp−ʈs>0. Our scheme, termed intelligent power control scheme, would work in matching through the in-synchronous form if both PU and SU achieve their respective goal. The essential info for PU can be SNRcr, and for SU, it can be SNRcr and SNRdr, while mr is the decision made during the time window ʈp+r−1T.ʈs+rt.Algorithm 2: Control power policy (DQN based).
InitializeԺb1 and then obtain m (1)
forr=1, r do
Sensing delay
chooseak=maxaQmr,a;ϑ0
obtainmr+1
end forFigure 4
Licensed and unlicensed users updated transmit power.


### 2.2. Delay Performance Using a Primary Sensor Network

A promising approach for CRN design can be the use of transmission data with the quality of services in wireless sensor networks. Designing a proper physical CRN, with effective and efficient spectrum allocation, sensing, and minimum potential interference, poses several challenges. Since license-free spectra are crowded in CRN, they are affected by uncontrolled interference, and hence, real-time traffic is recommended with the CRNs for the future. Figure3(a) presents the sensing delay that occurred in the sensing network. It can be seen that there are several SUs on a single PU node. The sensing delay for a U2-U1 connection is less than that for a U3-U2-U1 connection. This is due to the extra sensing delay to sense and get information for an extra link.The direct U3-U1 link is not obvious for the system. It checks the optimal link for U3 to connect with U1, and during that process, it depends on the response from U2. Similarly, the sensing delay will increase when there are several users on the primary node, and hence, information may be late.Figure3(b) represents a network of two cognitive radio users with a communication module. Here, we supposed that CR users use an estimated state for action and communicate its present state to the other user in case of an unsuccessful state. Both estimator 1 and estimator 2 estimate their corresponding X1e and X2e. In a normal situation, there is no need for communication. CR user 1 is working based on its own state X1, and CR user 2 estimated state X2e. When X2 is received from CR user 2, comm module 1 broadcasts X1 to CR user 2 if ∣X1−X1e∣>h1, where h1 is the defined threshold. Similarly, a communication mechanism and estimation are designed at CR user 2 and other CR users.


### 2.3. CRN Consensus Criteria under Communication Delay

Let transfer of message by the nearest agentm be received by agent n with a sensing delay T, which is similar to a network with a sensing delay of fixed one-hop communication. The algorithm of such consensus is given in the equation below.
(17)χmt=∑nεZmhmnχmτ−T.−χmτ−T.m.For getting an average consensus, a weight undirected graphG has been supposed in Equation (17). Therefore, the algorithm is
(18)χmt=∑nεZmhmnχnτ−T.−χmτm.The following form shows the collective dynamic of the network:(19)χt=−Lxt−Ṫm.Taking Laplace to transform,(20)As=Wssχ0m.Here, functionWs=In+I/sexp−sTL−1. For stability verification of Hs, the Nyquist criterion can be used. We can refer to the study as an approach that is similar in [40]. There is an upper bound sensing delay method for network stability that can maintain during time delay. The Equation (10) algorithm clarifies the problem of average consensus asymptotically for all early states or levels, if and only if 0≤Ṫ<π/2Ɣn, where Ɣn<2⍙. Refer to [36] for proof. A sufficient condition for the average consensus algorithm (17) is τ<π/4⍙. There may be a trade-off between sturdiness to sensing time delay and having a large max degree. A network having a great degree is normally considered a free-scale network. To study [41], small networks and random graphs are impartially active for sensing delay, in the absence of several degrees. consensus achievement of a buildup engineering network is a good example.


### 2.4. Simulation

Suppose four CR users in CRN after their traffic management; the communication topology in their information sharing is shown in Figure5.Figure 5
CR users in CRN.If we consider that all users have integrator dynamics, then by usingmx=−Lx, in which values of m changes regarding network dynamics mxt, where L=Lxy is the graph Laplacian of network, the performance without delay is shown in Figure 6(a). When delay has seemed to be in the network, it affects the performance of the CRN. Hence, consensus performance of the CRN could be seen in Figure 6(b) after communication delay without the proposed method. Although these responses are in consensus, their transient responses are very poor. Hence, the settling time is very large. So, for better performance, the designer should follow this proposed method to minimize the effects of time delay and sensing delay as well. Let a communication delay of 0.4 second between all users be the same; then, their consensus performance can be calculated by using the algorithm shown in Figure 7(a). This proposed method is also sufficient for large arbitrary communication delay of 0.4 sec. Thus, the consensus performance of the CR users with a large communication delay of 0.6 sec is shown in Figure 7(b).Figure 6
Consensus performance of CRN without the proposed method and with communication delay.Figure 7
Communication delay in CRN.
(a)
With large communication delay of 0.4 second
(b)
With communication delay of 0.6 sec


## 2.1. Intelligent Power Control of Spectrum Sharing

The distribution of system time is uniform, denoted as channel switching intermission. The presently employed channel develops unattainable culmination of the cooperative spectrum interval. When the sensor senses the second user, the channel might delay till the start of the next cooperative spectrum pause (if at least one user is available). In that case, both the user and sensor jump to the new channel. This process is termed as periodic switching (PS). Another cause may be that the central head may highlight the sensor if a new channel is available, as the prior channel is misplaced; this channel loss is stated as triggered switching (TS). The number of channel switching may be zero or one for periodic switching (PS); it depends whether the channel is present or not at the start of the cooperative spectrum interval. For a satisfactory transmission, the central station sends back an Automatic Control Key (ACK) to the sensors. If the sensor does not receive an ACK after a data packet transmission, it is assumed that the present channel is unavailable, and the transmission is stopped immediately. However, this kind of failure may happen due to channel fading which would cause a transmission failure on the CR sensor net. It is not a good practice to stop the transmission in this case, which would instigate needless interference with the PN (Primary Network). Therefore, BE (Best-Effort) data traffic and actual-time data traffic can be assisted in this case. A good example of this channel switching and traffic resource allocation can be found in [2].In the proposed work, SUs are assumed to take any action at each time step, such as for choosing transmit power from the earliest quantified power setP2 based on its present state. To analyse this, the Markov decision process (MDP) [37] is considered. Particularly, for instance, consider an action är=∂r+1 by SU in the state mr. Then, the next new state mr+1 is dependent on the present state mr and action of a decision-maker är. Here, mr and är are known. The following states will be independent of all earlier states and actions with the condition that
(8)mk≈∂an∨r⋯∂Nn∨rT.For a new state, a corresponding rewardňr∶=ňmr is assumed for the decision-maker är which can be mathematically expressed as
(9)n∨r≈z,ifSNRcr+1≥SNRdr+1≥ω′d,0,otherwise.In this work, “z” is assumed to be 10. It can be seen through simulation that the value of z should be sufficiently large to avoid the learning disturbance. Communication between a SU, a PU, and the sensors is shown in Figure 2(a). It is to be highlighted that the unlicensed user is supposed to distinguish whether communication between PT1 and PR1 is successful or not. This kind of information can be gained to monitor an acknowledged signal transferred PR1 for an indication of successful transmission from PT1. Figure 2(b) [15] shows the detached control architecture and is an object control system design in which there is a linear time-invariant (LTI) and multiple input-multiple output (MIMO) system.Figure 2
Unlicensed user and licensed network interactions and standard multiuser close loop.
(a)
Primary/licensed network
(b)
Standard multiuser close loopThe basic problem for the Markov decision process is to understand the policy for the decision-maker.(10)Uπmr≔∑a=rT−1γa−rn∨a,where π stipulates the action πm from the decision-maker. It is important to say that the purpose of SU is to understand a strategy π for the selection of its action är which is constructed on the present state mr in a method that discounted cumulative reward reduced maximum as studied in [38]. In Equation (10), “Ɣ” is the discount factor and T−1 is representing the time frame, at which the targeted state is touched. In this case, the targeted state is well defined, where SNRcr≥ὡi for i=1,2. The target is for studying optimal policy π∗ that maximizes Uπ, i.e.,
(11)π∗=argmaxUπm,∀m,It is complicated to directly learnπ∗. In the case of reinforcement learning, there is an alternative approach to solve Equation (11) through Q-learning. This alternative approach has been studied in [13]. Q-function (action value) is defined to determine the predictable reduced growing reward after the action ak+n, for state m. In such cases, the optimal policy would be built by choosing the action by the largest value in each state.By the updated Bellman equation,(12)Qm,a=n∨m,a+γmaxQm′,a′mThe elementary purpose ofQ-learning and several other reinforcement learning algorithms is to iteratively update the action value according to the value updating instruction. In Equation (12), “m′” is the state followed by smearing of action “a” to the present state “m.” The value iteration algorithm defined in Equation (12) approaches the best action value purpose. The number of states is limited for Q-learning, and at each state, the action value function is guessed separately. The Q-table is designed such that rows represent the states and columns represent the probable action state. One can choose an action from the Q-table as the maximum value of Qm,a through an optimal action state. However, the value of state function m is continuous due to arbitrary variation in the received signal. Therefore, the Q-learning method is unfeasible in this work since it is not convenient to consider an unlimited figure of states. To overcome this issue, DQN (Deep Q-Network) is opted. A brief study and proposed work of DQN are presented in [39].Different from the traditionalQ-learning technique, which is used to generate unlimited action value functions, “ϑ” is used here to express weights of Q-learning, while the Q-table is substituted by the deep neural network Qm,a:ϑ that would act as the action value function. Particularly, for an input “m,” DQN produces an E2-dimensional vector for selecting action a=Ժim from p2. When mr is given, the data used for Q-network training is generated as follows: we explore amorphous selected action with ϵk having the largest output Qmr,ar:ϑ0, where ϑ0 is used for denotation of the present iteration. Subsequently, the action an (r), SU gets a reward ϒ(r), a new statemr+1is obtained. This transit, dr∶=mr,ar,mr,mr+1, is held in the reiteration memory K. When enough transitions are collected in K, the training of the Q-network begins. Say O=300 evolutions, we casually choose a minibatch of transitions dii∈Ωr from K, and with adjustment of ϑ, DQN can be trained as given loss function is minimized:
(13)Eϑ≈1Ωr∑iε℧rQ′i−Qmi,a⋯i;ϑ2m.Ω
r is the index set of the irregular minibatch used at the rth iteration. The estimated value of the Bellman equation Q′i for the ith iteration is given by
(14)Q′i=n∨i+γmaxQsi+1,a..;ϑ0,∀iεΩrm.Different from the conventional supervised learning, the goal for DQN knowledge is different from that of the traditional approach.SU can select action after training, which gives a maximum projected valueQm,ä,ϑ∗. For simplicity, the DQN scheme is summarized in the power control scheme for SU. It would be clearer to highlight that during the training process of DQN, an SU needs the knowledge that satisfies the QoS (quality-of-service) necessities for the PU, and therefore, the SU is mollified. However, the only purpose of SU, after DQN training completion, is feedback from the sensors for the decision of the next transmit power. The junction problem of the supposed policy for power control is hence studied. Let “m” be a target state; then, if SU transmit power stays unchanged, it will be informal to say that the next state m′ is also a goalmouth state. Transmit power can result from either Equation (2) or (3), and as a result, PU will be updated. In another way, SU will ultimately acquire to select a diffuse power as m′ persists the goalmouth state. It can be concluded that once s achieves the target state, it will be in the goalmouth state till broadcast information is done. Now assume that there is a possibility of data loss because of the irregularity of data transmission and SU aims to take up for an innovative transmission; no long learning is required in this case. Rendering to control power policy, SU can select transmit power.Figure2(b) shows a standard multiuser closed loop representing power control in this case. Standard discrete time is considered for control system design. For a multi-input multioutput system called the MIMO system with linear time-invariant known as LTI, there are z input, w inputs, and h states.
(15)Zq+1=XAl+Qvl+Wlm,Cq=KAq+Hqz,where “q” represents the time index linked with T time sampling in the discrete time domain. X∈,K∈Ȑz∗n and Ȑn∗n,Q∈Ȑn∗m are output matrices and system input, and W. and H. are system measurements and disturbances, respectively. U.=u1.,⋯,uf.T and Y.=y1.,⋯,yz.T are expected to be barred, for example, ∣ui.∣≤giu,i=1,⋯,f and ∣yj.∣≤gjv,j=1,⋯,z, in which giu’s and gjv‘s are positive constant. For simplicity, all states are considered measurable, i.e., K=I. There is a possibility to design a feedback controller at state (1) through maximum input maximum output, which is shown as follows.
(16)VM=Mkqm,MMq−AC+Hqm.Algorithm 1: Power control policy-deep learning training based.
Initialize D with capacity O
Initialize networkQm,a,ϑ with variable weights ϑ=ϑ0
InitializeԺa and Ժb and then obtain m (1)
Forr=1, r do
UpdateԺar+1 via power control policy of PU (2) or (3)
With iterationsεk, choose an arbitrary action ak; otherwise, select ak=maxaQmr,a;ϑ0
Obtainmr+1 via arbitrary model (5) and detect reward nr
Store transitiondr∶=mr,ar,mr,mr+1, in D
Sensing delay
Repeat sensing delay
Ifr≥O then
Sample random minibatch of iterations fromDdii∈Ωr,
Here, theΩr index is uniformly selected at independent
Minimize loss function of 12, in which goal is given by (15) Q′i
Adjustϑ0=argminϑEϑ
End if
mr is the target state and then initialize ∂ar+1 and ∂br+1 and then gain mr+1
end if
end forThat is, Figure3(b) shows the spectrum sharing of the control system, which is well designed. So, the stability and performance of the system (z) could be definite through an approximate selection of V sampling time in Equation (16) and K as gain feedback design in Equation (15). A dynamic system is to be supposed (Equation (15)), there is a designed controller that works as a designed framework baseline.Figure 3
Sensing delay (sensing time) and spectrum sharing between users.
(a)
Sensing time delay
(b)
Spectrum between usersIn this paper, there is a consideration that the PU and SU update their power of transmission synchronously. However, we would like to highlight that our proposed scheme’s synchronous assumption is not a must. Consider that there is no strict synchronous occurrence in the time frame between PU and SU; both synchronize transmit power at the start of a timeframe. Figure4 represents the transmit power of a licensed and unlicensed user. PU adjusts its transmit power at time ʈp,ʈp+T,ʈp+2T⋯, whereas SU’s transmit power is updated at ʈs,ʈs+T,ʈs+2T⋯, where T is representing the time of each setting. Deprived of loss simplification, we consider thatT>ʈp−ʈs>0. Our scheme, termed intelligent power control scheme, would work in matching through the in-synchronous form if both PU and SU achieve their respective goal. The essential info for PU can be SNRcr, and for SU, it can be SNRcr and SNRdr, while mr is the decision made during the time window ʈp+r−1T.ʈs+rt.Algorithm 2: Control power policy (DQN based).
InitializeԺb1 and then obtain m (1)
forr=1, r do
Sensing delay
chooseak=maxaQmr,a;ϑ0
obtainmr+1
end forFigure 4
Licensed and unlicensed users updated transmit power.


## 2.2. Delay Performance Using a Primary Sensor Network

A promising approach for CRN design can be the use of transmission data with the quality of services in wireless sensor networks. Designing a proper physical CRN, with effective and efficient spectrum allocation, sensing, and minimum potential interference, poses several challenges. Since license-free spectra are crowded in CRN, they are affected by uncontrolled interference, and hence, real-time traffic is recommended with the CRNs for the future. Figure3(a) presents the sensing delay that occurred in the sensing network. It can be seen that there are several SUs on a single PU node. The sensing delay for a U2-U1 connection is less than that for a U3-U2-U1 connection. This is due to the extra sensing delay to sense and get information for an extra link.The direct U3-U1 link is not obvious for the system. It checks the optimal link for U3 to connect with U1, and during that process, it depends on the response from U2. Similarly, the sensing delay will increase when there are several users on the primary node, and hence, information may be late.Figure3(b) represents a network of two cognitive radio users with a communication module. Here, we supposed that CR users use an estimated state for action and communicate its present state to the other user in case of an unsuccessful state. Both estimator 1 and estimator 2 estimate their corresponding X1e and X2e. In a normal situation, there is no need for communication. CR user 1 is working based on its own state X1, and CR user 2 estimated state X2e. When X2 is received from CR user 2, comm module 1 broadcasts X1 to CR user 2 if ∣X1−X1e∣>h1, where h1 is the defined threshold. Similarly, a communication mechanism and estimation are designed at CR user 2 and other CR users.


## 2.3. CRN Consensus Criteria under Communication Delay

Let transfer of message by the nearest agentm be received by agent n with a sensing delay T, which is similar to a network with a sensing delay of fixed one-hop communication. The algorithm of such consensus is given in the equation below.
(17)χmt=∑nεZmhmnχmτ−T.−χmτ−T.m.For getting an average consensus, a weight undirected graphG has been supposed in Equation (17). Therefore, the algorithm is
(18)χmt=∑nεZmhmnχnτ−T.−χmτm.The following form shows the collective dynamic of the network:(19)χt=−Lxt−Ṫm.Taking Laplace to transform,(20)As=Wssχ0m.Here, functionWs=In+I/sexp−sTL−1. For stability verification of Hs, the Nyquist criterion can be used. We can refer to the study as an approach that is similar in [40]. There is an upper bound sensing delay method for network stability that can maintain during time delay. The Equation (10) algorithm clarifies the problem of average consensus asymptotically for all early states or levels, if and only if 0≤Ṫ<π/2Ɣn, where Ɣn<2⍙. Refer to [36] for proof. A sufficient condition for the average consensus algorithm (17) is τ<π/4⍙. There may be a trade-off between sturdiness to sensing time delay and having a large max degree. A network having a great degree is normally considered a free-scale network. To study [41], small networks and random graphs are impartially active for sensing delay, in the absence of several degrees. consensus achievement of a buildup engineering network is a good example.


## 2.4. Simulation

Suppose four CR users in CRN after their traffic management; the communication topology in their information sharing is shown in Figure5.Figure 5
CR users in CRN.If we consider that all users have integrator dynamics, then by usingmx=−Lx, in which values of m changes regarding network dynamics mxt, where L=Lxy is the graph Laplacian of network, the performance without delay is shown in Figure 6(a). When delay has seemed to be in the network, it affects the performance of the CRN. Hence, consensus performance of the CRN could be seen in Figure 6(b) after communication delay without the proposed method. Although these responses are in consensus, their transient responses are very poor. Hence, the settling time is very large. So, for better performance, the designer should follow this proposed method to minimize the effects of time delay and sensing delay as well. Let a communication delay of 0.4 second between all users be the same; then, their consensus performance can be calculated by using the algorithm shown in Figure 7(a). This proposed method is also sufficient for large arbitrary communication delay of 0.4 sec. Thus, the consensus performance of the CR users with a large communication delay of 0.6 sec is shown in Figure 7(b).Figure 6
Consensus performance of CRN without the proposed method and with communication delay.Figure 7
Communication delay in CRN.
(a)
With large communication delay of 0.4 second
(b)
With communication delay of 0.6 sec


## 3. Results and Discussion

The transmit power (in watts) for PU and SU is selected from a predefined setPc=Pd=1/20,0.1/1,⋯,0.4/1, and the noise power N1 and N2 at PR1 and SR2, respectively, are set to 0.01 W. For simplicity, channel advancement from the primary transmitter and secondary transmitter to PR1 and SR2 is considered to be hxy=1,∀x,y. To achieve the lowest SNR (signal-to-noise ratio), productive reception for PU and SU is adjusted to ὡc=11/9 and ὡd=7/10, respectively. The presence of transmit power ∂a,∂b can be easily noted, which means that the quality of the PU-SU system is satisfactory. Additionally, several active sensors remain N, which would accept the acknowledged signal strength information to help SU to adapt to the power control policy. There is uniformly distributed distance dxy between the sensor node and Txi transmitter in a pause range of 100,300 in meters.For the action value approximation function, we used the deep neural network (DNN), which contains feedforward layers. The number of these layers is three and is entirely linked. These hidden layers contain neurons 256, 256, and 512, respectively. For the 1st and 2nd layers, rectified linear units are working as an action function, where the ReLU layer output will be 0 or raw for negative input. The activation function is used in the case of the 3rd layer, and the Adam algorithm is used to update weight φ, while the minibatch size is set to 256. Here, it is considered that rerun memory K holdsNK=400. In each iteration, training of φ starts, and 300 evolutions/transitions are considered for each K. The number of transitions is adjusted to r=105. Exploring the probability of a new-fangled action, action reduces with an increase in the number of iterations, and as the iterations increase to a sufficiently large value, it reduces from 0.8 to 0. Additionally, at reiteration r, it is supposed that ϵ¯r=0.81−r/K.There is access to deep reinforcement learning in our article, specifically, success rate, loss function, and average number. The transition step is being used as transition number functionr has been analysed. Here, the presentation is judged through two metrics, which are transition steps and average number. Success rate computation is in standings of the figure of successful trails to total figure of easily turn’s a ratio. Here, assume a productive trail if “m” transfers to a target in 20 time frames. In the case of a productive trail, the average number of time frames needs to reach a target which termed as transition step average number.During the exercise process, loss function can be calculated as presented in [14]. After learning iteration r, SU may use the trained network for interaction with PU. Network performance is determined standings of an average number of transitions and success rates. Outcomes are average over 103 freely turns, where the chance start state is chosen for each track. The numerical results have been divided into two cases.


### 3.1. Case 1 (without Delay)

Case one shows that by the guidance of learned power control policy, transmit power of SU/unlicensed user can intelligently be adjusted like final target may be touched since somewhat preliminary target indoors rare figure of transmission steps. In Figure8(a) (success rate vs. no. of iterations for case 1), the number of sensors used is 3, in which we set according to the number of iterations k, σn=∂aԺJcn+∂bmJdn/3. With the increase in σn to reduce the number of sensors, the loss function value becomes larger. It is good policy to achieve the average number of transition steps and loss function vs. no. of iterations similar to those shown in Figures 8(b) and 8(c). Figure 8 reveals the strength of the deep reinforcement learning approach.Figure 8
Success rate, loss function, and average number of transitions vs. iterations using no. of sensors (3).
(a)
Success rate vs. no. of iterations
(b)
Loss functions vs. no. of iterations
(c)
Average no. of transition series vs. no. of iterations


### 3.2. Case 2 (with Delay)

Case 2 shows the sensing time delay (r+k) as shown in Figure2. This sensing time delay has been found in the SU policy as in Equation (5). This sensing time delay occurs when PU shares transmit power or spectrum with SU; then, there is the penetration of SUs on the primary node that causes sensing delay during the sharing of transmit power or spectrum. In this case, power control performance reduces. Figure 9(a) shows the success rate vs. no. of iterations. Figure 9(b) shows the loss function vs. no. of iterations, and Figure 9(c) shows the average no. of transitions vs. no. of iterations. We showed the recital of the DQN-based power control method in which a secondary power control policy is employed by the PU as in Equation (4) which seems additionally traditional. The target of learning a suitable power control policy is in Figure 9 which shows the loss function, success rate, and an average number of transition steps vs. k. Here, we used the number of sensors which is 10. σn=∂aԺJcn+∂bmJdn/10. It is to be observed that a greater number of iterations are required for getting a success rate. In our policy, the average number of transition steps is 2.5 for achieving the target state. Here, the PU used a second policy which only permits transmit power for an increase or decrease in the signal level at each step. For this purpose, we need more steps. The explained method sustains a supposed performance loss in the case of fewer sensors deployed; this happened due to random variations in observation states which built various conditions less unique from one another and save the agents from learning of an active strategy. Random variation effect can be neutralized by the use of more sensors.Figure 9
Success rate, loss function, and average number of transitions vs. iterations using no. of sensors (5) and iterations (10000).
(a)
Success rate vs. iterations
(b)
Loss functions vs. iterations
(c)
Average no. of transition series vs. iterationsFigure10(a) shows the success rate vs. iterations, Figure 10(b) shows the loss function vs. iterations, and Figure 10(c) shows the average no. of transition steps vs. no. of iterations. For the purpose of training, we used a number of sensors (10). σn=∂aԺJcn+∂bmJdn/10. In this sample, the plot is run with 30000 iterations and a delay of 2 samples. Here, in the success rate plot, the effect of delay is clear. This sensing delay is because of the penetration of SUs on the primary node during the sharing of spectrum. In this case, power control performance will reduce.Figure 10
Success rate, loss function, and an average number of transitions vs. iterations using several sensors (10) and iterations (30000).
(a)
(b)
(c)Figure6(a) shows the consensus performance of CRN showing results without the proposed model sensing delay. However, these are poor transit responses of consensus performance. All agents reached their steady-state value after nearly 100 seconds. However, the settling time is large. So, for progressing performance, one should track this projected technique to lessen the effects of communication and sensing time delay as well. If there is the consideration of communication and sensing delay amid entirely CR operators, suppose that sensing delay of 0.4 second inside whole operations is identical. The assumed method is enough for the representation of large-scale sensing delay in the CR network. Figures 7(a) and (7)(b) show the communication delay of 0.4 sec and 0.6 sec, respectively, in a CRN.


## 3.1. Case 1 (without Delay)

Case one shows that by the guidance of learned power control policy, transmit power of SU/unlicensed user can intelligently be adjusted like final target may be touched since somewhat preliminary target indoors rare figure of transmission steps. In Figure8(a) (success rate vs. no. of iterations for case 1), the number of sensors used is 3, in which we set according to the number of iterations k, σn=∂aԺJcn+∂bmJdn/3. With the increase in σn to reduce the number of sensors, the loss function value becomes larger. It is good policy to achieve the average number of transition steps and loss function vs. no. of iterations similar to those shown in Figures 8(b) and 8(c). Figure 8 reveals the strength of the deep reinforcement learning approach.Figure 8
Success rate, loss function, and average number of transitions vs. iterations using no. of sensors (3).
(a)
Success rate vs. no. of iterations
(b)
Loss functions vs. no. of iterations
(c)
Average no. of transition series vs. no. of iterations


## 3.2. Case 2 (with Delay)

Case 2 shows the sensing time delay (r+k) as shown in Figure2. This sensing time delay has been found in the SU policy as in Equation (5). This sensing time delay occurs when PU shares transmit power or spectrum with SU; then, there is the penetration of SUs on the primary node that causes sensing delay during the sharing of transmit power or spectrum. In this case, power control performance reduces. Figure 9(a) shows the success rate vs. no. of iterations. Figure 9(b) shows the loss function vs. no. of iterations, and Figure 9(c) shows the average no. of transitions vs. no. of iterations. We showed the recital of the DQN-based power control method in which a secondary power control policy is employed by the PU as in Equation (4) which seems additionally traditional. The target of learning a suitable power control policy is in Figure 9 which shows the loss function, success rate, and an average number of transition steps vs. k. Here, we used the number of sensors which is 10. σn=∂aԺJcn+∂bmJdn/10. It is to be observed that a greater number of iterations are required for getting a success rate. In our policy, the average number of transition steps is 2.5 for achieving the target state. Here, the PU used a second policy which only permits transmit power for an increase or decrease in the signal level at each step. For this purpose, we need more steps. The explained method sustains a supposed performance loss in the case of fewer sensors deployed; this happened due to random variations in observation states which built various conditions less unique from one another and save the agents from learning of an active strategy. Random variation effect can be neutralized by the use of more sensors.Figure 9
Success rate, loss function, and average number of transitions vs. iterations using no. of sensors (5) and iterations (10000).
(a)
Success rate vs. iterations
(b)
Loss functions vs. iterations
(c)
Average no. of transition series vs. iterationsFigure10(a) shows the success rate vs. iterations, Figure 10(b) shows the loss function vs. iterations, and Figure 10(c) shows the average no. of transition steps vs. no. of iterations. For the purpose of training, we used a number of sensors (10). σn=∂aԺJcn+∂bmJdn/10. In this sample, the plot is run with 30000 iterations and a delay of 2 samples. Here, in the success rate plot, the effect of delay is clear. This sensing delay is because of the penetration of SUs on the primary node during the sharing of spectrum. In this case, power control performance will reduce.Figure 10
Success rate, loss function, and an average number of transitions vs. iterations using several sensors (10) and iterations (30000).
(a)
(b)
(c)Figure6(a) shows the consensus performance of CRN showing results without the proposed model sensing delay. However, these are poor transit responses of consensus performance. All agents reached their steady-state value after nearly 100 seconds. However, the settling time is large. So, for progressing performance, one should track this projected technique to lessen the effects of communication and sensing time delay as well. If there is the consideration of communication and sensing delay amid entirely CR operators, suppose that sensing delay of 0.4 second inside whole operations is identical. The assumed method is enough for the representation of large-scale sensing delay in the CR network. Figures 7(a) and (7)(b) show the communication delay of 0.4 sec and 0.6 sec, respectively, in a CRN.


## 4. Conclusions

Machine learning and CR intelligence have a good capability to understand and adapt to the wireless environment. In wireless communication, machine learning techniques are linked with CR technology. The cognitive radio system which consists of PU and SU is well studied; in this paper, we explained the problem of spectrum sharing of PU and SU in CRNs, and also, we introduced sensing delay in communication. Because there was a common concept that there is no cooperation between PU and SU, PUs adjust their transmit powers on their own transmit control power policy. In this article, we discussed the consensus performance and introduced aQ-learning or deep reinforcement learning method for SU to study for the adjustment of its transmit power so that ultimately both the PU and SU have the ability to transmit respective data fruitfully with the essential qualities of services. Our numerical results showed that the considered learning method is healthy against the random variations in the state variation and within few numbers of steps. We can get our target from an initial state, and also, in numerical results, we showed sensing delay that is because of the number of SUs when PU transmits spectrum with the SU; then, there is a rush of SU on the primary node that caused sensing delay; it is because of a lot of several users. All agents reached their steady-state value after nearly 100 seconds. However, the settling time is large. The given method is enough for the representation of large-scale sensing delay in the CR network.



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*Source: 7125482-2021-02-19.xml*