System Model
 SSDF Attack: Reference and Mathematical Expressions
 Proposed System Model
 A Novel Schema
 Proposed Method
 An “Improvedapriori” Algorithm
 Implementation of the Proposed Method
 Performance Evaluation of the Accuracy
 Discourse and Performance Rating
 Basic Simulation Configuration
 Conclusions
 References
 Appendix I: Proof of Error Probability, Pе
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 missdetection 

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 missdetection 

Probability of false alarm for an extended sensing across an entire slit 

Probability of missdetection 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 missdetection 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 [16]:
Where H„ refers to PU that is unavailable, H denotes that the PU is available, and d (t_{0}) is the SU’s collected signal at time t_{0}. Let m (t_{0}) be the PU’s transferred signal, g is the profit obtained by the channel, and w (t_{0}) is the additive white Gaussian (AWG) noise. The collected energy observation in the energy detector is: E_{ob} = X?=i I d(t_{0}) I^{2}, 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„_{h}under two hypotheses H,_{h} then H_{[ }is as follows [18]:
Where 3o=2v, <5o=4v, di= 2v(a + l), 5^{2} =4v(2a + l), and the SU received signaltonoise ratio (SNR) is a. By comparing the energy monitoring with a limited threshold (p, the SU binary decision d is given as:
Let P_{0} be the probability of assumptions. The detection probability p_{d}, and the false alarm probability p_{f} 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 d_{e} 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 p_{a }is extended from 0 to 1. Let 0 indicate a peak case of never attack and 1 denote an alwaysattack 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 KoutofN rule and similarity ratio test rule [18]. This is used to execute individual and collaborating sensors. The KoutofN 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 illwill SUs of Byzantine/SSDF attacks, classifies them into three types and incorporates with the blind scenario.
The first type is a 'smart illwill 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 illwill 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 illwill 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, P^{A}o j e {0,1}
For Truthful nodes:
For Byzantine sensors:
Where P^{AL}(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 a_{k} <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:
H_{0}: PU is not active (absent)
Н_{0}: 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 [25] can be expressed as:
So it becomes, P_{fa} = P,_{ta}
By algebraic expression it can be simplified as [25]:
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 alwaysattack 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 illwill users. The ‘novel’ method along with the ‘improvedapriori’ 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 ‘itnprovedapriori’ algorithm along with the ‘novel’ method, where H_{0} = 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 “Improvedapriori” Algorithm
This chapter uses the “improvedapriori” (iapriori) algorithm for the possible improved detections which are higher than the existing ones. The KoutofN rule is incorporated in the pseudocode below, as follows:
Apriori (A, e)
(SI7), = find_frequent_l_itemsets(T) ;
/ / construct N_{2}by self  join
n_{2} = (su^^su),
(SU)_{2} = items in N_{2} > 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)] [1] a (SD), [2] = (SU)] [2]
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 N_{k};
N_{k} = n u N_{k};
/ / Intersection between the target transaction TID set to calculate the support (SU)fk = New  quick_support_count {N_{k}, к counter / (SU)_{u}_S_{f}) ;
Answer = U_{k}(SU)_{k};
New_quick_support_count(N_{k}, к counter / (SU)_{u}_S_{f}) ;
{for all S_{f}N e Nf
N.(SU)_{u}_S_{t} = N_{k}_{1}.(SU)_{a}_S_{f}nN_{1}.(SU)_{u}_S_{e }N.sup = Length(N_{k}. (SU)_{u}_S_{t}) ;
If N.sup < min_sup Delete N from N_{k}
(SU)_{(} к = {N e N_{k} w. sup > min_sup}}
Prune 1 (SU)_{C}
for all S_{f} (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 N_{k} 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 S_{f} is the sensor that takes the selected two nodes. Then, N_{f} 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 N_{k} 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 improvedapriori (also known as iapriori) algorithm is suggested. The procedure is as follows [26]:
 1. The scanned reports are considered, to get the к counter for a SU.
 2. Rationalize (St/T1, before the SU report N_{k} comes. Then, count all the SU occurred in N_{f}1, and delete SUs, w'hich is less than k1 [15].
 3. Through the convergence strategy, count the nodes of right SU using N_{t }based on the к counter of (SU)_{fl} and SU of N,.
 4. Then cease the algorithm, if (SU)_{f}
[16].
This algorithm reduces the number of assailant SUs and the time to count all the truthful nodes decreases. The iapriori contains a receiver id (k counter) for the distributed CR systems [26]. 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 iapriori algorithm, the parameter N takes the (St/), and (St/)_{;}. The infinite number
TABLE 6.2
The Receiving к Counter of iapriori
к counter/(SU)_{U} 
s, 
к counter/(SU)_{U} 
Secondary Users S_{f} 
K+ 
SU, SU, 
K+6 
SU, SU, SU, 
K+1 
SU, SU, 
K+1 
SU, SU, 
K+i 
SU, SU, 
K+ 8 
SU, su_{4} 
K+4 
SU, SU,. SU,. su_{4} 
K+9 
su_{4} su_{6} 
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 reassess 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 iapriori method, and P,^ = P_{0}(g = 0, Я, j is a misseddetection 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 P_{u} (R= 1 G = 1, //„) = Pf Likewise, the suggested missdetection probability is:
Performance Evaluation of the Accuracy
The adjacent existing sources (H_{t} (busy) or else H_{0} (idle)) are evaluated in the spectrum sensing execution, ie., in the probability of missdetection and false alarm. The preferred one is the probability of error [21]. The probability of error P_{e} in (6.32) is given as:
The probability that the real channel condition is P_{{)} ( H_{0}) and P_{0} (H). Due to the enlarged sensing of the spectrum, Эо, Э: and 5_{0}, 5i are r times of Э_{0}, Э and 5_{0}.
Suggestion 1: The threshold (p_{r} is the defense scheme of SU that will reduce the error probability P_{e} as follows:
And,
and
The above formulation of к is estimated by the iapriori 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, Pf^{x} = 1, P„f_{d} = 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 e_{f} and the probability of miss detection e_{md}. The assigned sensor is x, e {T, AL}. The sensor outcome assigns x, for S^{XI} whose identification operation is calculated as (P^{xl}d, 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 [9], t_{0}th for the sensor reputation value ft)’^{7} is calculated as:
If/= 0 then 5^{Л} (г)*Ф (t) or/ = 1 for S" (t)= Ф (?). The binomial distribution is modified and a Gaussian estimation [9] is given as:
Where, d_{AL}= S, ^{AL}, 8^{2}AL = S, ^{AL} (1 ^{AL}),^{AL} = S, ^{T}, 8f = S, X^{r}(lX^{7}') The assigned sensor is:
The threshold is в and P_{t}„ is an assailant sensor probability that is incorrectly assigned as truthful.
Let P_{u}, be the truthful sensor probability that is incorrectly assigned as an assailant one. Both of them are separately calculated as:
Let n^{AL} and n^{T} indicate the rate of truthful and assailant sensors. Then, n^{AL} + rc^{T} = 1 that contains the possibility of wrongly detecting sensors which is assigned as P_{mm }as follows:
A maximum posteriori probability rule simplifies the KoutofN rule. Therefore, the global probability of false alarm and missdetection [25] 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 01. The time bandwidth for the extended sensing of SUs ranges from 100 to 500 bps. The probability of false alarm is 0.08. Then P_{c} = 0.01, constitutes the worse for WiMax network [9] and P_{e} = 0.001 is adopted for WiFi networks that do not include the results of P_{e} = 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 iapriori technique.
Figures 6.6 and 6.7 represent the performance of the s0/l technique and the iapri ori method given enlarged sensing. The proposed technique performs better than the existing s0/l.
FIGURE 6.4 Performance of iapriori with the existing methods in different attack probabilities.
FIGURE 6.5 Performance of iapriori with the existing methods in different attack populations.
FIGURE 6.7 Performance of proposed iapriori 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 iapriori scheme in blind and nonblind scenario.
In Figure 6.8, the trusted node transmission rate is calculated from the existing method of N_{s0}/ 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 nonblind scenario. The sO/1 result is taken from article [21] and the proposed iapriori scheme is implemented according to the blind scenario in Equation (6.27). For a nonblind 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 5GCR 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 NS3, a numerical simulation that confirms that the proposed method has better performance, especially in the case of a major or minor assailant sensor.
References
 1. J. Rodriguez, “Fundamentals of5G Mobile Networks: Security for 5C Communications,” West Sussex, UK: John Wiley & Sons Ltd., 2015, pp. 207219.
 2. E. Hossain, and M. Hasan, “5G Cellular: Key Enabling Technologies and Research Challenges,” IEEE Instrumentation & Measurement Magazine, vol. 18, no. 3. June 2015. pp. 1121.
 3. J. Mitola, “Cognitive Radio: an Integrated Agent Architecture for SoftWare Define Radio," Ph.D. dissertation. Dept. Teleinfo., Royal Inst. Of Tech. (KTH). Stockholm, Sweden, 2000.
 4. A. Mesodiakaki. F. Adelantado. L. Alonso, and C. Verikoukis, “Energy Efficiency Analysis of Secondary Networks in Cognitive Radio Systems,” IEEE Int. Conf. on Comm.. Selected Areas in Communications Symposium, Budapest, Hungary. June 913, 2013. pp. 41154119.
 5. H. Li, X. Cheng, K. Li, C. Hu. and N. Zhang. “Robust Collaborative Spectrum Sensing Schemes in Cognitive Radio Networks,” IEEE Transactions on Parallel and Distributed System, vol. 25, no. 8, August 2014. pp. 21902200.
 6. E. Nurellari, D. McLernon, and M. Ghogho, “A Secure Optimum Distributed Detection Scheme in UnderAttack Wireless Sensor Networks,” IEEE Transaction on Signal and Information Processing Over Networks, vol. 4, no. 2. June 2018, pp. 325337.
 7. A.H.S. Magdalene, and L. Thulasimani, “Analysis of Spectrum Sensing Data Falsification (SSDF) Attack in Cognitive Radio Networks: A Survey,” Journal of Science and Engineering Education, vol. 2, 2017. pp. 89100.
 8. H. Luan. O. Li. and X. Zhang, “Cooperative Spectrum Sensing with Energy Efficient Sequential Decision Fusion Rule.” IEEE Wireless and Optical Communication Conference, pp. 14, 2014.
 9. A.A. Alkheir, and H.T. Mouftah. “Sequential HardDecision Fusion for Agile Cooperative Spectrum Sensing.” IEEE International Conference on Communication Workshop, pp. 10141019. 2015.
 10. S. Peng, W. Zheng, R. Gao. and K. Lei, “Fast Cooperative Energy Detection Under Accuracy Constraints in Cognitive Radio Networks,” Wireless Communications & Mobile Computing, pp. 18, 2017.
 11. C.I. Badoi, N. Prasad, V. Croitoru. and R. Prasad, “5G Based on Cognitive Radio,” Wireless Personal Communication Journal, vol. 57, no. 3, April 2011. pp. 441464.
 12. Ericsson. 5G Radio Access. Uen 284 233204 Rev C. Stockholm. 2016.
 13. R. Chen, J.M. Park, Y.T. Hou. and J.H. Reed, “Toward Secure Distributed Spectrum Sensing in Cognitive Radio Networks,” IEEE Communication Magazine, vol. 46, no. 4. April 2008. pp. 5055.
 14. V. Sucasas, A. Radwan. S. Mumtaz, and J. Rodriguez, “Effect of Noisy Channels in MACBased SSDF CounterMechanisms for 5G Cognitive Radio Networks,” International Symposium on Wireless Communication System, Brussels, Belgium, August 2528. 2015, pp. 15.
 15. J. Lu, P. Wei. and Z. Chen. “A Scheme to Counter SSDF Attacks Based on Hard Decision in Cognitive Radio Networks,” WSEAS Transaction on Communication, vol. 13. 2014, pp' 242248.
 16. S. Kim, H. Cha, J. Kim, S.W. Ко. and S.L. Kim, “SenseandPredict: Harnessing Spatial Interference Correlation for Cognitive Radio Networks,” IEEE Transactions on Wireless Communications, vol. 99 (accepted), April 2019, pp. 117.
 17. F. Song, Y.T. Zhou, L. Chang, and H.K. Zhang. “Modeling SpaceTerrestrial Integrated Networks with Smart Collaborative Theory.” IEEE Networks, vol. 33, no. 1, January 2019. pp. 5157.
 18. S. Bhattacharjee, R. Keitangnao, and N. Marchang, “Association Rule Mining for Detection of Colluding SSDF Attack in Cognitive Radio Networks.” International Conference on Computer Comm. & Info., Coimbatore. India. 2016.
 19. R. Amutha Priya. and S. Nandhakumar, “Attack Prevention for Spectrum Sensing Data Falsification Attacks in Cognitive Radio Networks Using Arc.” International Journal of Advanced Research in Science, Engineering and Technology, vol. 2. no. 3. March 2015, pp. 486490.
 20. M. Khasawneh, and A. Agarwal, “A Collaborative Approach Towards Securing Spectrum Sensing in Cognitive Radio Networks,” Procedia Computer Science, vol. 94. no. 2016, December 2016. pp. 302309.
 21. J. Wu. Y. Yu. T. Song, and J. Hu, “Sequential 0/1 for Cooperative Spectrum Sensing in the Presence of Strategic Byzantine Attack,” IEEE Wireless Communications Letters, vol. 8, no. 2, April 2019, pp. 500503.
 22. J. Feng, M. Zhang, Y. Xiao, and H. Yue, “Securing Cooperative Spectrum Sensing Against Collusive SSDF Attack Using XOR Distance Analysis in Cognitive Radio Networks”, Sensors, vol. 18, no. 2, January 2018, pp. 114.
 23. J. Zhang, L. Cai, and S. Zhang. “Malicious Cognitive User Identification Algorithm in Centralized Spectrum Sensing System", Future Internet: MDPI Journal, vol. 9. no. 79. November 2017, pp. 113.
 24. H. Wang, Y. Li, and T.C. Chang, “An Enhanced Cooperative Spectrum Sensing Scheme for AntiSSDF Attack Based on Evidence Theory," Microsystem Technologies, vol. 24. no. 6, June 2018, pp. 28032811.
 25. J. Wu. T. Song. Y. Yu. C. Wang, and J. Hu, “Generalized Byzantine Attack and Defense in Cooperative Spectrum Sensing for Cognitive Radio Networks" IEEE Access, vol. 6, August 2018, pp. 5327253286.
 26. X. Yuan, “An Improved A Priori Algorithm for Mining Association Rules,” AIP Conference Proceeding Journal, vol. 1820. no. 1, Mar. 2017, pp. 0800051 0800056.
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 (p_{p}.
Case 2: к > 0, then if,/  Aik > 0, (p_{r} is one of zero and a larger solution to h (
P_{c}((p)
get a smaller value, if/  Aik < 0, then (p_{p} = 0.