# System Model

Table 6.1 shows the symbols and expressions used for the proposed work.

TABLE 6.1

Symbols and Expressions Used for the Proposed Work

 Letter Denotation Number of sensors Truthful sensor count formulated in the к counter Channel real states Sensor reports Probability of false alarm Probability of miss-detection Malicious sensor probability conducting attacks False alarm probability conducting attacks Detection probability conducting attacks Truthful sensor’s false alarm probability Assailant sensor’s false alarm probability Universal report Probability of detection in the truthful sensor Probability of detection in an assailant sensor Universal probability of a false alarm Universal probability of a miss-detection Probability of false alarm for an extended sensing across an entire slit Probability of miss-detection for an extended sensing across an entire slit Suggested source results Attack strength in percentage Assailant sensor probability that is incorrectly assigned as a truthful one Truthful sensor probability that is incorrectly assigned as an assailant one Probability of false alarm for the suggested scheme Probability of detection for the suggested scheme Probability of miss-detection for the suggested scheme The universal extension of a particular location for the false alarm probability The universal extension of a particular location for the detection probability

Individual sensors operate on energy detection sensing to get a limited decision. An adjacent sensor S„ raises the spectrum sensing possibility. The SU’s sensing report is corporate and then a universal decision G is constructed for the objective passage. For every sensor, a binary hypothesis test problem is computed in the spectrum sensing as follows : Where H„ refers to PU that is unavailable, H denotes that the PU is available, and d (t0) is the SU’s collected signal at time t0. Let m (t0) be the PU’s transferred signal, g is the profit obtained by the channel, and w (t0) is the additive white Gaussian (AWG) noise. The collected energy observation in the energy detector is: Eob = X?=i I d(t0) I2, where v = ТВ, and where ТВ is the product of time and bandwidth in the energy detection of CRN. For the central restricted theorem, when v is large enough (e.g., v » 10), and a Gaussian arbitrary inconstant E„hunder two hypotheses H,h then H[ is as follows : Where 3o=2v, <5o=4v, di= 2v(a + l), 52 =4v(2a + l), and the SU received signal-to-noise ratio (SNR) is a. By comparing the energy monitoring with a limited threshold (p, the SU binary decision d is given as: Let P0 be the probability of assumptions. The detection probability pd, and the false alarm probability pf are formulated as: The Gaussian (/operation is Q(x). The probability of the missed detection is P,L = 1 - P,f ■ The truthful sensor announces the genuine decision de for the data fusion to the SU. Even if an assailant sensor commits wrong decisions/to mislead the SU to construct the falsified conclusion as, f * d,,.The assailant probability pa is extended from 0 to 1. Let 0 indicate a peak case of never attack and 1 denote an always-attack case, respectively. Finally, the sensing of assailant sensor is calculated as: The SU executes the universal report G for report gathering. The common blending rules are K-out-of-N rule and similarity ratio test rule . This is used to execute individual and collaborating sensors. The K-out-of-N rule is suitable for all sensors, but the SSDF sensor makes the rule more ineffective and tends to make a wrong decision.

## SSDF Attack: Reference and Mathematical Expressions

Multiple attackers will collaborate to falsify the data. Each attacker has a unique ID. This attack pattern is a popular collusive attack, especially found in CSS to create errors in the sensing data. This is called as SSDF attack. The SU’s sensing function for each case is not permitted due to the shadowing which is shown in Figure 6.1. FIGURE 6.1 SSDF sensor at the time of SU data fusion.

This chapter addresses the ill-will SUs of Byzantine/SSDF attacks, classifies them into three types and incorporates with the blind scenario.

The first type is a 'smart ill-will SU’. That means, if the node senses 1 (occupied) from the primary base station (BS), it will send 0 (vacancy) to the data fusion center (DFC) as a result and contrariwise. The second type is 'always occupied ill-will SU’. This always sends 1 to the DFC as being an occupied channel. This is not as smart as the first assailant, but it causes a denial of service (DOS) attack, which means that the channel is constantly not available for the truthful SUs. And the third type is ‘always vacant ill-will SU’. This sends 0 to the DFC, which denotes that the SU assumes that the channel is always available. But sometimes the channel is occupied and a collision takes place. The SU uses more energy and time for searching another frame. A truthful node moves its own data and sends its outcome to another node or FC. A Byzantine sensor alters the transmission with some decisions. A mathematical model for the Byzantine attack is assumed as: Pj, Pj_0, Pjf, PAo j e {0,1}

For Truthful nodes: For Byzantine sensors: Where PAL(S = i'| G = j) is the assailant node probability that sends / as a sensor result and receives j from the global decisions. The actual decision is j. If a node is an attacker, but its ascendants are not, it requires a Byzantine outcome due to another Byzantine which is a neutralized one. The node to the FC will have at least one SSDF or Byzantine, Xf=i ak <1. But the number of Byzantines in any other way to the FC cannot be greater than 1. The SSDF CR identity is unknown and is found as follows: a is the probability of a single received detection at the FC which is from a Byzantine. The FC binary hypothesis test is formulated as:

H0: PU is not active (absent) Н0: PU is active (present) FC is mindful of the presence of Byzantine attacks, but it will not differentiate truthful and assailant nodes. An assailant causes the FC to make an incorrect decision regarding the presence or absence of the PU. In the given hypothesis, each SU’s sensing result is added to the conditional independent and identical distribution. Therefore, the blind condition  can be expressed as: So it becomes, Pfa = P,ta

By algebraic expression it can be simplified as : Nearly a half part of the assailant user can completely blind the FC, when a = = 1.

It is the minimum rate that makes the FC blind. This assumption shows that the low malicious rate has a always-attack strategy that enables the existing studies [20, 24] to escape the blind problem.

# Proposed System Model

## A Novel Schema

In 5G assumptions, user devices travel in a large number of wireless devices and they do not know about the honest and ill-will users. The ‘novel’ method along with the ‘improved-apriori’ method will solve this problem. Each frame of cognition contains two stages: the sensing and the accessing phase of the spectrum. The accessing phase relies on the universal report results. The SU will access if the universal decision has the result ‘the PU is absent’. Otherwise, the SU has to wait for the upcoming frame for the process to be done. This is a general cognitive process. If the SU approaches the PU channel, one of two tasks will occur to transfer the information successfully. Otherwise, it may collide with the PU communication. If the PU is not available, the universal report is right, and ‘success’ is possible; or else, it may cause failure. This can be used as a feedback for the defense performance.

If the SU waits for the upcoming frame, one of two tasks will occur: i.e., an ‘idle’ or ‘busy’ PU channel. It may lose due to a fake universal decision report. The restricted SU sensing execution will be upgraded by expanding the time of sensing. FIGURE 6.2 An execution of an ‘itnproved-apriori’ algorithm along with the ‘novel’ method, where H0 = H, indicates the original channel condition. R denotes the proposed result, and C is the universal decision report.

But, at the time of the waiting stage, the SU tracks the sensing process and enlarges the restricted SU’s sensing results as shown in Figure 6.2. The enlarged sensing outcome is used as usable feedback.

## Proposed Method

### An “Improved-apriori” Algorithm

This chapter uses the “improved-apriori” (i-apriori) algorithm for the possible improved detections which are higher than the existing ones. The K-out-of-N rule is incorporated in the pseudocode below, as follows:

Apriori (A, e)

(SI7), = find_frequent_l_itemsets(T) ;

/ / construct N2by self - join

n2 = (su^^su),

(SU)2 = items in N2 > min_sup,- For (к = 3; (set),.! * 0; к + +)

{ / / further prune (SU),.!

Prunel( (SU)f-2) ;

(SU)X e (SU)f,(SU)x(SU)f;

If((SU), [lj = (SU)]  a (SD),  = (SU)] 

A... (SU), [k - 2] = (su), [k - 2j A (SU), [к - l]

< (SU)] [k - lj)

N = (SU), U (SU)] ;

If (k - l) - subsets s of n g (SU)f_1 then delete N from Nk;

Nk = n u Nk;

/ / Intersection between the target transaction TID set to calculate the support (SU)fk = New - quick_support_count {Nk, к counter / (SU)u_Sf) ;

New_quick_support_count(Nk, к counter / (SU)u_Sf) ;

{for all SfN e Nf

N.(SU)u_St = Nk-1.(SU)a_SfnN1.(SU)u_Se N.sup = Length(Nk. (SU)u_St) ;

If N.sup < min_sup Delete N from Nk

(SU)( к = {N e Nk |w. sup > min_sup}}

Prune 1 (SU)C

for all Sf (SU)f e (SU)k;

If count (SU)f in (SU)k < k;

Then delete all (SU), from (SU)k return (SU)f

In this code, all the SU sensor reports S are divided into / and j parts. Each part takes a maximum of two reports in S. Let к be the counter that takes these two nodes to check the similarity. If the nodes are similar, it removes the malicious node. Let S„ be the number of sensor and Nk counts the number of SUs, which are not similarly under checking in к counter. Let/be the parameter that selects any of these two nodes and Sf is the sensor that takes the selected two nodes. Then, Nf is the counter that counts the/pair series and (Su)f denotes the entire SU pair series. Let и be the parameter that takes an apriori algorithm (A, £) for parameter Nk and (SU)j. Then it is counted as (SU)„ and (SU)k is the number of SUs к counter.

To annul the repeated scan of distributed data, the improved-apriori (also known as i-apriori) algorithm is suggested. The procedure is as follows :

• 1. The scanned reports are considered, to get the к counter for a SU.
• 2. Rationalize (St/T-1, before the SU report Nk comes. Then, count all the SU occurred in Nf-1, and delete SUs, w'hich is less than k-1 .
• 3. Through the convergence strategy, count the nodes of right SU using Nt based on the к counter of (SU)fl and SU of N,.
• 4. Then cease the algorithm, if (SU)f .

This algorithm reduces the number of assailant SUs and the time to count all the truthful nodes decreases. The i-apriori contains a receiver id (k counter) for the distributed CR systems . In the algorithm, T denotes the item set and min_sup is the parameter w'hich helps to know about the minimum support for honest SU. In the i-apriori algorithm, the parameter N takes the (St/), and (St/);. The infinite number

TABLE 6.2

The Receiving к Counter of i-apriori

 к counter/(SU)U s, к counter/(SU)U Secondary Users Sf K+ SU, SU, K+6 SU, SU, SU, K+1 SU, SU, K+1 SU, SU, K+i SU, SU, K+ 8 SU, su4 K+4 SU, SU,. SU,. su4 K+9 su4 su6 K+5 SU,. SU,. SU, ff+lO SU,. SU,

of SUs will be united up to N, and R is the outcome to get the right SU in the whole SU pairs.

A 10 к counter and a 6 SU set are shown in Table 6.2. The minimum level of SU taken is 2.

## Implementation of the Proposed Method

The R helps the SU to re-assess the restricted sensing execution for every individual sensor. The false alarm probability of the proposed one is calculated as: The universal report of G e {O(inert), l(full)} and the probability of false alarm is given by, P,Pl' = G = 1, #<,) . Then R e {O(inert), l(full)} is the result of the proposed i-apriori method, and P,^ = P0(g = 0, Я, j is a missed-detection probability.

It contains P{) (R = Я, | G = 0) = 1. Otherwise, the SU executes an enlarged sensing of the spectrum, even when the decision is G = 1. The result of sense is over at the total slit, then Pu (R= 1| G = 1, //„) = Pf Likewise, the suggested miss-detection probability is: ### Performance Evaluation of the Accuracy

The adjacent existing sources (Ht (busy) or else H0 (idle)) are evaluated in the spectrum sensing execution, ie., in the probability of miss-detection and false alarm. The preferred one is the probability of error . The probability of error Pe in (6.32) is given as: The probability that the real channel condition is P{) ( H0) and P0 (H). Due to the enlarged sensing of the spectrum, Эо, Э: and 50, 5i are r times of Э0, Э| and 50.

Suggestion 1: The threshold (pr is the defense scheme of SU that will reduce the error probability Pe as follows: And, and The above formulation of к is estimated by the i-apriori algorithm. Then the estimation problem is solved by the maximum likelihood estimation, which follows:  FIGURE 6.3 Enlarged sensing indicates the probability of detection fiSand probability of false alarm Pf~' for the restricted SNR is -10 dB.

For a proof, see Appendix I in this chapter, the real universal decision (UD), i.e., Pf and PHi. Then (p = 0 for the suggested source, Pfx = 1, P„fd = 1. Figure 6.3 indicates the suggested sources under different assailant probability P,„ and an assailant populations in к counter.

Let Ф be the source for probability of false alarm ef and the probability of miss- detection emd. The assigned sensor is x, e {T, AL}. The sensor outcome assigns x, for SXI whose identification operation is calculated as (Pxld, Pj'1). The possibility for S*1 * Ф is calculated as: In (6.42), £x> denotes the actual execution of the sensor and is assigned as X/. The universal report , t0th for the sensor reputation value ft)’7 is calculated as: If/= 0 then 5Л| (г)*Ф (t) or/ = 1 for S" (t)= Ф (?). The binomial distribution is modified and a Gaussian estimation  is given as: Where, dAL= S, AL, 82AL = S, AL (1- AL),AL = S, T, 8f = S, Xr(l-X7') The assigned sensor is: The threshold is в and Pt is an assailant sensor probability that is incorrectly assigned as truthful.

Let Pu, be the truthful sensor probability that is incorrectly assigned as an assailant one. Both of them are separately calculated as: Let nAL and nT indicate the rate of truthful and assailant sensors. Then, nAL + rcT = 1 that contains the possibility of wrongly detecting sensors which is assigned as Pmm as follows: A maximum posteriori probability rule simplifies the K-out-of-N rule. Therefore, the global probability of false alarm and miss-detection  under the rule for the data fusion is given as: # Discourse and Performance Rating

## Basic Simulation Configuration

The local SNR for the SUs is taken as -lOdB. The chance for the PU channel equaling the full origin is O.l. The truthful detector performance is adjusted as Pj = O.l and Pj = 0.9. The probability of the assailant is P„, and an assailant detector ranges from 0-1. The time bandwidth for the extended sensing of SUs ranges from 100 to 500 bps. The probability of false alarm is 0.08. Then Pc = 0.01, constitutes the worse for WiMax network  and Pe = 0.001 is adopted for Wi-Fi networks that do not include the results of Pe = 0.1, which indicates the rough wireless conditions.

Figures 6.4 and 6.5 represent the enhanced performance of the proposed method compared to different existing techniques with different attack probabilities and populations. The proposed method greatly reduces the error probability of a CSS.

From Figures 6.4 and 6.5, we can conclude that the sequential 0/1 scheme is the competing technique to be compared with the proposed method. Therefore, for all the following simulations, s0/l strategy is implemented and compared with the i-apriori technique.

Figures 6.6 and 6.7 represent the performance of the s0/l technique and the i-apri- ori method given enlarged sensing. The proposed technique performs better than the existing s0/l. FIGURE 6.4 Performance of i-apriori with the existing methods in different attack probabilities. FIGURE 6.5 Performance of i-apriori with the existing methods in different attack populations.  FIGURE 6.7 Performance of proposed i-apriori method in enlarged sensing detection. FIGURE 6.8 Performance of transmission rate over time. FIGURE 6.9 Correct sensing ratio of existing sO/1 and proposed i-apriori scheme in blind and non-blind scenario.

In Figure 6.8, the trusted node transmission rate is calculated from the existing method of Ns0/ in Equations (6.5 and 6.6) and from the proposed method Equation (6.37) and (6.38) through the к counter.

In Figure 6.9, for voting rule k, the existing and proposed result will be taken according to the blind and non-blind scenario. The sO/1 result is taken from article  and the proposed i-apriori scheme is implemented according to the blind scenario in Equation (6.27). For a non-blind scenario, only «and /5 values are implemented by eliminating the p value in (6.25) and (6.26).

# Conclusions

This chapter focuses on two new methods for the security of CSS in CRN, which results in the security of 5G-CR technologies. The proposed method confronts SSDF attack in CR as w'ell as future trends of modern technologies like IoT, 5G, Vanet, etc. The chapter’s simulation is done in NS-3, a numerical simulation that confirms that the proposed method has better performance, especially in the case of a major or minor assailant sensor.

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# Appendix I: Proof of Error Probability, Pе

From (6.12), taking the differential with respect to we have: Let (6.14) be 0, we have: Here,  Where Similarly, at the same time: Case 1: к < 0, then have,/ - Aik > 0, hence the highest outcome is the optimum value (pp.

Case 2: к > 0, then if,/ - Aik > 0, (pr is one of zero and a larger solution to h (Pc((p) get a smaller value, if/ - Aik < 0, then (pp = 0.