It is verified that the collision penalty limits successfully suppress each of the attacks. Simulations reveal that SU throughput in a CSS system in the face of PUEAs is maximized.

## Background

The PU can impose fines on honest SUs and also restrict their further use of its spectrum [22]. As a result, the PU can punish the honest SUs and the PUE can take advantage of the situation.

## Areas of Research in CRs

*Signal Propagation**Signal Processing**Cooperative Spectrum Sensing**Security Issues in CSS*

As a result, the throughput of the SUs is degraded and the interference on the PU seriously increases. On the other hand, if the FC is misled about the absence of the PU and broadcasts it as 'present', the SUs will stop their transmissions.

## Motivations and Problem Statements

### Problem 1

In the first part of the thesis, we aim to overcome these limitations of the schemes proposed in [2].

Problem 2

Problem 3

## Contributions of the Thesis

Individual SSDF Attacks

Collusion SSDF Attacks

PUEAs

## Organization of the Thesis

*Chapter 2**Chapter 3**Chapter 4**Chapter 5**Chapter 6*

We propose the optimal dataset size to maximize the outlier rejection capacity of the Dixon test. We maximize the SU by limiting the interference with the PU to obtain the optimal weights.

## Basic SS Concepts

*Energy Detection**Cyclostationary Feature based Detection**Matched Filter and Waveform based Detection**Matched Filter based Sensing**Waveform based Sensing**Covariance based Sensing Methods**Covariance Matrix based Sensing**Autocorrelation based Sensing**Eigen Value based Sensing*

Covariance-based sensing exploits the difference in the covariance of the received signal when the PU signal is present and when it is absent [ 72 ]. This difference is used for formulating the decision statistics in covariance-based mechanisms.

## Security Issues in SS

The choice of an SS mechanism depends on the knowledge of the signal at the receiver and the channel and the SNR conditions. Some detection mechanisms illustrated above provide high performance given the signal knowledge available with the receiver (examples are the matched filter detectors, the cyclostationary function detectors, and the waveform-based detectors).

## SSDF Attacks in CR Communications

### Active Methods

In [18], MUs first geolocate the SU position from their detection reports. Here, the authors believe that knowledge about the MU strategy is not available.

### Passive Methods

The authors in [105] focus on the dilemmas that arise in the coordination due to the attacks. The attack power is defined here as the ratio between the MUs and the total number of SUs in the system.

## PUEAs in CR Communications

### Active Methods

The location information of the PU was used to distinguish between the signal characteristics of the PU and the PUE. In [108], the authors further improve the tagging system of [20] by making it independent of the PU signal.

### Passive Methods

Applying the test to multiple blocks extends the scope of the Dixon test to multiple outlier detection. Brings improvement in the performance of the Dixon's test without a significant increase in the complexity.

## System Model

### Hypothesis Testing for PU Detection

The integration in (3.2) can be approximated by the sum of the square signal samples. 3.4) whereγi is the non-centrality parameter and is the sum of the mean values of theiri(m) samples. Each SU sends its calculated energy value ei(m) to the FC through an error-free reporting channel.

### Performance Parameters

The evaluation of an SS system is done by plotting convergence regions (ROC curves). However, to separately represent the shifts inserted into the Pf a and Pd curves by the MU data, we fitted the conventional ROC curves by plotting each separately with λ.

### The Uncertainty in SS and the Attack Process

To plot the ROC curves in Section 3.7, we perform Monte-Carlo simulations with the aforementioned steps over a set of different Pf a values covering the range 0≤Pf a ≤1 and obtain the corresponding Pd values.

## Detection of MUs as an Outlier Detection Problem

### Grubbs’ Test

This is because significant increases observed in the reports of the SUs would suggest that the PU started to transmit with the particular recurrence. Similarly, when the reports from the SUs show a significant decrease, it indicates that the PU has stopped carrying out.

Boxplot Test

## Dixon’s Test for Outlier Detection

### Outlier Factor in the Dixon’s Test

A test statistic expressed as the ratio of the above distance e[N]−e[N−1] to the range of the data e[N]−e[1] remains invariant of the location (mean) and scale (variance) of the data sample . Interestingly, both the Grubbs test and the Dixon test were published in the same issue of the Annals of Mathematical Statistics.

### Calculation of the Critical Value (C v )

The critical values for Dixon's test are calculated by integrating (3.31) forr = 0 toR, and the equation is evaluated using numerical quadrature approach using Legendre polynomials. The value of R is calculated using the split method for a given value of the cumulative distribution function (CDF) using the initial values CDF=0, R=0 and CDF=1, R=1.

## Proposed Method

### Scheme 1: Three-Point Dixon’s Test over Non-Overlapping Blocks

Then, the Dixon test is applied to each group to detect the possible outlier value in each group. This deterioration is due to the fact that the applicability of the Dixon test is limited to only one outlier in a group.

### Scheme 2: Three-Point Sliding Window Dixon’s Test

The limitation above motivated us to propose the three-point sliding window Dixon's test. Under this scheme, each will be subjected to the test three times in 3-point Dixon's test.

## A Note on the Complexity of the Proposed Schemes

If any of the tests declare ei as an outlier, the SU is considered a MU.

## Simulation Results and Performance Assessment

### Evaluating the Robustness of the Dixon’s Test over Small Data Samples

Figures 3.6 and 3.7 show the comparisons when 1 MU is present, while Figures 3.8 and 3.9 show the comparisons for the presence of 2 MUs.

### Performance Evaluation in Suppressing a Single MU

These values are compared to those of the CSS without a MU and the CSS with the MU removed using the 20-point Dixon's test. This is because each SU in scheme 2 is subjected to the Dixon test three times compared to once in scheme 1.

Performance Evaluation in Suppressing Multiple MUs

## Conclusion

This difference in the cross-correlation of MU and SU detection reports is used for MU identification and elimination. Malicious behavior analysis is done by observing MU utilities.

## System Model

*System Model and Assumptions**Decision Fusion Rule**Evaluation Parameters and Conditions**Assumptions*

AND rule: According to this rule, the FC decides for the presence of the PU only when all the N SUs report 1 to the FC. OR rule: Through this rule, the FC decides for the presence of the PU if only one US 1 reports to the FC.

## Proposed Scheme

Bound on C P for Sharing the Spectrum by the PU

### Optimal Decision Fusion Rule

In the next section we find a nopt aimed at maximizing SU throughput. As mentioned earlier, the probability of successful transfer for the SU in the presence of the PU is negligible, hence PeP U ≈1.

## Bounds on C P for Attack Prevention

### Avoiding Malicious Strategies when the FC declares H 1

*Avoiding (H, M )**Avoiding (M,M)*

In Phase 2, MUs gain nothing by playing H, which means obeying the FC rather than broadcasting. It will be useless for MUs to ignore FC and not transmit in Phase 2.

### Avoiding Malicious Strategies when the FC declares H 0

*Avoiding (M,H)*

It can be seen from (4.24) that the value of CP is large, since its lower bound is UP U. To solve this problem, in the next section, we show with the help of Game Theory that MUs lose a lot as they play maliciously and the proposed CP ensures avoidance of any malicious activity and complete safety of honest SUs from unfair penalty.

## The Best Strategy for the SUs

This implies that the utility obtained by each SU when at least one of them is malicious is negative. Note that although the utility GUi(1,0) is positive, none of the malicious strategies will cause the SUs to achieve this value.

## Conclusion

Then, we briefly describe the existing works, their limitations, and the significance of the SU throughput maximization problem in the presence of PUEs in Section 5.2. Subsequently, in Section 5.4, we formulate the maximization problem for the SU throughput while providing sufficient protection for the PU.

## PUEAs

In this chapter, we consider the second kind of attack mentioned in Chapter 1: the primary user emulation attack (PUEA) [55]. The honest SUs mistake a PUE's signal to come from the PU and stop their transmissions.

## Approaches to Combat PUEAs

The authors in [56] and [57] proposed a belief propagation based defense strategy, which uses the location information of the PU and the RSS of the PUEs. The location identification based mechanisms distinguish the direction of arrival (DOA) of the received signal from the PUE and the PU.

## System Model, Sensing Mechanism and Parameters

### System Model

5.1), where hpi(j) denotes the channel coefficient of the PU-ith SU path, hei(j) denotes the channel coefficient of the PUE-ith SU path, xp(j) and xe(j) denote the PU and PUE signals assumed to that they are BPSK modulated, ui(j) denotes the noise at the SU, which is assumed to be a circularly symmetric complex of Gaussians (CSCG), and γp and γe the SNR of the PU to SU and PUE to SU paths, respectively. Our goal is to consider eis at FC to maximize SU throughput.

### Characterization of the Parameters

*Probabilities of False Alarm and Miss Detection**Throughput of an SU (G i (w, λ))**Effective Interference to the PU (I ef f (w, λ))*

The decision regarding the PU presence is made at FC by comparing E with a decision threshold λ. When the PU spectrum is detected free, it is allocated to the SUs depending on the followed spectrum allocation policy [171].

## Maximization of the SU Throughput under PUEAs

The problem of optimizing T or T1 for maximizing SU throughput in the presence of PUE has not been investigated so far to our knowledge. Designing Weighted CSS: Our goal in this chapter is to design a weighted CSS for maximizing SU throughput while limiting PU interference.

## Obtaining Optimal Weights for Performing CSS

### Calculation of w 0

Intuitively, a low weight value should be given to the energy of the SU which has good channel relations with the PUE. It can be seen that w0p exploits the virtue and adversity of SU channel conditions with PU and PUE.

### Obtaining w ∗

All vertices except wB,wS and wW lie on the line adjacent to wS and wB. The next step is to calculate the centroid 'c' of all points except wW. Now, with each iteration, the simplex moves toward w∗. If the opposite is the case, wW is replaced by wr and the reflection process starts again.

### Average Throughput and Interference

*Average Throughput**Average Interference*

At the beginning of the algorithm, the maximum number of iterations for the algorithm to converge must be specified. If the number of iterations or the number of function evaluations in an iteration exceeds the specified maximum value, the algorithm stops and the final value obtained should be taken as the optimal value.

## Experimental Results and Performance Evaluation

### Static Transmitters and Receivers

On the other hand, the environment between PU and SU is still considered Rayleigh faded. Therefore, the PU-SU channel is considered Rician faded, while the PUE-SU channel is considered Rayleigh faded.

### Transmitters and Receivers in Motion

In Figure 5.17, the relative motion of the ith SU and the PUE is assumed to be in opposite directions (θ= 180), with the same relative velocity. Therefore, Figure 5.17 shows lower values of SU throughput compared to Figure 5.18.

## The Reason for using the NMA

Similarly, in the evaluation done in Fig. 5.19, only the PUE moves towards the ith SU, indicating case 2. The magnitude of the relative velocity was taken as v = 40 mi/h, and accordingly fd is obtained as 110.31 Hz, and the Doppler range is 220.62 Hz.

## Conclusion

In this thesis, we have focused on the effects of PUEAs on the turnover of SUs. Our objective was to reduce the damage caused by PUE to the throughput of SUs.

## Suggestions for Future Research

### Suppression of Multiple Malicious Users

Such a redesign of SU throughput maximization, which is required by the presence of PUE, has been implemented for CSS. Our goal was to combine the data of participating SUs in such a way that the effects of PUEA on SU flow are suppressed.

Suppressing Collusion Attacks

Suppressing PUEAs

### Security issues in frequency selective fading channels

It can also be seen that when considering the frequency-selective channels, a frequency shift will appear between transmitter and receiver. The study of security issues on frequency selective channels and noise correlation model can be an area for our future research.

### Research on military applications

Varshney, “Cooperative spectrum sensing in the presence of byzantine attacks in cognitive radio networks,” IEEE Transactions on Signal Processing, vol. Nguyen, “Surveillance strategies against primary user emulation attack in cognitive radio networks,” IEEE Transactions on Wireless Communications , vol.

The ever increasing annualized cost of frequency spectrum in India [1]

Centralized CSS

Decentralized CSS

Spectrum Sensing Data Falsification Attack

Primary User Emulation Attack Model

Periodic Sensing by SUs

Unreliability in Spectrum Sensing

Box Plot method for outlier detection

Comparison of MU detection performance of the N-point Dixon’s tests with Grubbs

Comparison of MU detection performance of the N-point Dixon’s tests with Grubbs

MU detection of the proposed schemes and the scheme in [2] for a single high reporting

Periodic Sensing

Primary User Emulation Attack Model

Periodic Sensing

Working simplex with reflection, contraction and expansion points