Combined Fusion Rules in Cognitive Radio Networks Using Different Threshold Strategies

Abstract

Compromising the performance and overhead is a crucial factor in designing cognitive radio networks (CRNs). One way to achieve this goal is to combine different fusion rules for a CRN with multiple clusters of cognitive radios (CRs). This paper proposes a new adaptive combination algorithm to balance between detection performance of a CRN and its reporting overhead through combining different fusion rules over the CRN. Initially, the paper describes how to combine hard decision, i.e., one-bit, and soften-hard decision, i.e., two-bit, fusion rules over a CRN with multiple clusters of CRs using different strategies. Simple combination and modified combination strategies, to consider a trade off between performance improvement and incurred reporting overhead, are considered. The paper adopts different threshold strategies to implement the proposed combinations. Moreover, the proposed algorithms are examined under the Rayleigh fading channel model and simulated to investigate their detection performance and to compare their detection performance with existing works. The simulation results show that the adaptive threshold strategy outperforms the two proposed fixed threshold strategies and conventional fusion schemes.

1. Introduction

The available spectrum resources are limited and insufficient to satisfy the spectrum requirements, i.e., high sampling rates and large bandwidth, for the newly emerging communication technologies, such as Internet of Things (IoT) and 5G. Moreover, the regulatory bodies in every country impose rigid spectrum assignments to the licensed users, i.e., Primary Users (PUs), to use designated portions of spectrum with exclusive rights to own them over the whole country. Those spectrum assignments resulted in exacerbating the problem, since the PUs do not allow other unlicensed users, i.e., Secondary Users (SUs), to share their bands during their inactivity periods. Furthermore, the spectrum shortage increases by the ever increase in the number of users of those technologies demands more spectrum resources. Dynamic Spectrum Access (DSA) principle was proposed as a solution to relieve the spectrum shortage [1] by allowing SUs to opportunistically utilise PUs’ bands during their inactivity period and leave those bands once the PUs recommence their activities without causing an interference to the PUs. The DSA principle is implemented by using Cognitive Radio (CR) technology which operates through four functional components, namely, spectrum sensing, spectrum sharing, spectrum management and spectrum mobility [2].

Spectrum sensing is the key functional component by which a SU detects the existence of a PU over a designated spectrum band. PU detection can be performed using different spectrum sensing approaches, such as Energy Detector (ED), matched filter, feature detection techniques, eigenvalue-based techniques, etc. The simple hardware and low computational requirements made ED as the most widely used approach to perform spectrum sensing. However, the detection performance of ED significantly deteriorates in low signal to noise ratio (SNR) scenarios, noise uncertainty situations, and severe radio conditions, such as multipath fading and shadowing [3]. In such cases, collaboration between SUs significantly improves the detection performance of individual SU [4]. The collaboration process is called Cooperative Spectrum Sensing (CSS) and requires to establish common control channel for information exchange between SUs in a Cognitive Radio Network (CRN) which results in increasing the bandwidth requirement, energy consumption and time delay. Moreover, the attaining improvement in detection results also in reducing the spectrum efficiency, i.e., throughput, due to increasing the global probability of false alarm [4,5]. Therefore, it is mandatory to trade off between the attaining detection improvement, i.e., gain of CSS, and the incurred overhead, i.e., cost of CSS. Note that the global probability of detection of a CRN is generally used to assess its detection performance, where higher probability of detection reflects more PU protection from CRs’ interference which is the essential condition for DSA. Clustering is a promising technique to balance between the cooperation gain, and cooperation cost. Therefore, Cluster-Based CSS (CBCSS) has been extensively adopted in CRN research works. The survey in [6] classified CBCSS techniques into three classes which are:

• Detection performance gain oriented schemes. These schemes mainly focus on improving the detection performance, i.e., probability of detection and/or throughput. For instance, optimizing the fusion rule employed in a CRN [7,8,9], optimizing the sensing time [10,11] fall in this class.
• Overhead reduction-oriented schemes which focus on reducing the incurred overhead including energy consumption, time cost and bandwidth occupation. Reducing the overhead can be implemented using different approaches, such as saving sensing time technique [12], reducing the required bandwidth technique [13], and saving the consumed energy in reporting observations technique [14].
• Combined metric-based schemes which balance the trade-off between the detection performance and the incurred overhead simultaneously. The balance can be achieved by combining two different fusion rules over the same cluster or CRN as shown in [15,16,17,18,19,20,21].

The combined metric-based schemes class is the main focus of this paper. The work in [15] combined a soft decision fusion, i.e, Selection Combining (SC) scheme, and one bit hard decision majority rule by optimizing the hierarchical structure of the cluster. The work in [16] proposed a weighted combination of two-bit decision and one-bit decision rule over multiple clusters in a CRN, while the work in [17] proposed an algorithm that combines soft decision rules, i.e. Equal Gain Combining (EGC) and SC schemes over a cluster using the hierarchy of the cluster.

On the other hand, different combination mechanisms have been proposed in [18,19,20,21]. The work in [18] proposed three modules system which are local detection, data reconstruction module and global decision. In the local detection module, each CR in the cluster detects the existence of a PU using ED and forward their observations using either one-bit or two-bit decision rule to the Fusion Center (FC). The data reconstruction module is implemented using a multi-bit quantization and the FC estimates the received observation through a data reconstruction module based on the statistical distribution of the observations. Finally, global decision module is to make the final decision by computing the sum of inverse quantization values of the received observations. In [19], the CRN is divided into two levels, cluster level and CRN level. In the cluster level, CH employs Likelihood Ratio Test (LRT) technique, i.e., soft decision, to extract cluster’s while the system level, the FC employs a weighted decision fusion rule, i.e., hard decision rule, to come up with a final detection decision. Likewise, in [20], each CR employs ED to sense the PU existence and forwards its observation using a simple quantization-based multi-bit data soft fusion rule instead of forwarding local one-bit hard decision results or original observation statistics, to the FC. This work allows a large number of CRs to forward their observations over a control channel with a limited bandwidth. Similarly, the work in [21] proposed a non-uniform quantized data fusion (N-QDF) rule to minimize the reporting overhead for ED-based CSS in CRNs. An algorithm with variable number of QDF bits is proposed in that work to balance between saving data and minimizing the reporting overhead, where employing small QDF bit results in losing the information while employing large QDF bit leads to increase the overhead. A compressed QDF bits are transmitted over the control channel. However, the works in [18,19,20,21] add computational complexity, such as quantizer and data compressor, and some of them require a prior knowledge of the statistical distribution of the observation, such as in [18]. Note that designing a quantizer for n bits requires $2^n-1$ thresholds which remarkably incurs extra computational complexity.

This motivated us to propose a combination of two-bit and one-bit rules using different threshold strategies without adding extra hardware and computational complexity. In this paper, three threshold strategies are employed, the first strategy employs the estimated SNR of each cluster to determine which fusion rule should use either one-bit rule or two-bit rule as illustrated in Algorithm 1. The second strategy is performance-based strategy to determine eligible clusters to participate in making the final decision about the PU existence as provided in Algorithm 2. Lastly, the third strategy employs an adaptive threshold to maintain detection error rate minimum and to allow all clusters to participate in making decisions as shown in Algorithm 3. The proposed strategies outperform the existing works in terms of total probability of detection over different radio conditions, i.e., different SNRs. Moreover, the proposed strategies attain better probability of detection than the existing works when other scenarios are employed, such as varying the number of CRs in a cluster, increasing sensing time and varying fusion parameters.

The contribution of this work can be summarized as follows:

• Proposing a framework of combining hard decision, i.e., one-bit, and softened-hard decision, i.e., two-bit, using three different threshold strategies to improve the detection performance of a CRN with multiple clusters while reducing the reporting overhead over the control channel between FC and CHs.
• Investigating the impact of increasing sensing time, and number of CRs in each cluster to verify the robustness of the proposed strategies.
• Investigating the impact of fusion parameter K on the performance of the proposed strategies. For this purpose, for N users, different values of K have been used , i.e., half voting $K=\lceil \frac{N}{2}\rceil$, majority voting $K=\lceil \frac{N}{2}\rceil +1$, and minority voting $K=\lceil \frac{N}{2}\rceil -1$, where the most existing works used only the majority voting rule.

Note that this work is different from our previous works [16,17] where our work in [17] combines EGC and SC as a soft decision rule with one-bit hard decision rule over the hierarchical structure of the clusters, while our work in [16] proposes a weighting strategy to combine two-bit and one-bit rule using different weights, where FC assigns a weight for each cluster based on its estimated SNR.

The rest of the paper is organized as follows. Section 2 provides a background of cognitive radio network. Section 3 provides a description of the system model. Section 4 describes the proposed combination algorithms. Section 5 shows how to compute the reporting overhead. Section 6 illustrates and discusses the results of implementing the proposed algorithms .Finally, Section 7 presents the conclusions.

2. Theoretical Background of Cognitive Radio Networks

2.1. Detection Performance of a Local Sensing

The availability of the detected channel can be modeled as the following binary hypotheses:

$$\begin{array}{ccc}{H}_0:\hfill & x=w\hfill & \hfill \left(idlechannel\right),\\ H_1:\hfill & x=y+w\hfill & \hfill \left(busychannel\right),\end{array}$$

where x is the detected signal, w is additive white Gaussian noise and y is the received PU signal, while $H_{i=0,1}$ represent the binary hypotheses of absence and presence of a PU, respectively.

The criteria assessment of a CR’s detection performance are the probability of false alarm and the probability of detection. The probability of false alarm, $P_f$, is defined as a probability of falsely detecting the presence of the PU when the channel is idle. Minimizing $P_f$ is a goal in order to maximize spectrum efficiency. In other words, increasing $P_f$ results in losing available spectrum opportunities. The $P_f$ can computed as:

$$P_f=\frac{\Gamma \left(\frac{M}{2},\frac{\lambda }{2}\right)}{\Gamma \left(\frac{M}{2}\right)},$$

(1)

where M is the time-bandwidth product (i.e., $\frac{M}{2}$ is the number of samples), $\lambda$ is the detection threshold, $\Gamma (.)$ is the Gamma function and $\Gamma (.,.)$ is the incomplete Gamma function.

The probability of detection, $P_d$, is defined as a probability of sensing the existence of the PU correctly when the channel is busy. In other words, $P_d$ reflects the accuracy of detection and maximizing $P_d$ is an ultimate goal. The $P_d$ can be computed as

$$P_d=\frac{\Gamma \left(\frac{M}{2},\frac{\lambda }{2(1+\gamma )}\right)}{\Gamma \left(\frac{M}{2}\right)},$$

(2)

where $\gamma$ is the instantaneous SNR.

Equation (2) shows that $P_d$ is dependent on $\gamma$ which varies according to the channel conditions. For instance, if a CR experiences Rayleigh fading channels, the $P_d$ is determined by averaging Equation (2) over the probability density function (PDF) of $\gamma$ provided by

$$f\left(\gamma \right)=\left(\frac{1}{\overline{\gamma }}\right)exp\left(\frac{-\gamma }{\overline{\gamma }}\right),\gamma \ge 0$$

(3)

where $\overline{\gamma }$ is the average SNR.

In general, the expression of the average $P_d$ in case of Rayleigh fading, $P_{d,Ray}$ can be as [22]

$$P_{d,Ray}={\int }_0^{\infty }\frac{\Gamma \left(\frac{M}{2},\frac{\lambda }{2(1+\gamma )}\right)}{\Gamma \left(\frac{M}{2}\right)}\left(\frac{1}{\overline{\gamma }}\right)exp\left(\frac{-\gamma }{\overline{\gamma }}\right)d\gamma ,$$

(4)

2.2. Detection Performance of Cooperative Sensing

Owning to severe radio conditions, such as multipath fading, shadowing and noise uncertainty, collaboration between CRs provides a solution to alleviate the impact of those conditions on the detection performance of individual CRs [3,4]. There are three collaboration schemes, they as centralized, non-centralized or relay-assisted. In a centralized scheme, every individual CR detects the existence of the PU and then forwards its local observation to a central entity which gathers observations and fuses them to extract a final decision about the existence of the PU. In non-centralized scheme, individual CRs detect the existence of the PU and then share their local observations between each other and come up with a final decision about the existence of the PU through a consensus. Finally, in relay-assisted scheme, after detection, a CR amplifies or decodes its observation and forwards it to another CR [23].

This paper focuses on the centralized CSS scheme using using several fusion rules. After detection, CRs forward their observation as either hard decision, i.e., one-bit as ’0’ or ’1’, or soft decision, i.e., energy form as a stream of bits. However, the latter requires a large bandwidth and incurs extra computational complexity for decision fusion in the central entity. Therefore, to reduce the bandwidth and computational complexity, a hard decision is the most widely used. However, the employment of hard decision reduces the accuracy of detection. To improve the performance of hard decision, two-bit scheme, i.e., softened hard decision scheme, has been developed such that detection performance improves with a little increase in the required bandwidth and complexity [18,24,25]. More details are provided below.

2.2.1. One-Bit Hard Decision Scheme

A CR makes its hard decision as a one-bit, D, by comparing the detected energy to the sensing threshold, $\lambda$, as shown in Figure 1. The sensing threshold, $\lambda$, is determined based on a predefined probability of detection. At the central entity, the gathered decisions are fused using the K-out-of-N rule which makes a decision using only K observations out of N available observations in the system. A proper selection of fusion parameter, K, plays an important role in optimizing the detection performance of the CSS. For instance, if $K=1$, the K-out-of-N operates as OR-Rule which significantly improves the global detection performance while reduces the spectrum efficiency. If $K=N$, the K-out-of-N operates as AND-Rule which significantly improves the spectrum efficiency while reduces the global detection performance. Therefore, to balance between improvement in detection performance and spectrum efficiency, K is selected as $K=⌈\frac{N}{2}⌉$) which is called half voting-rule, where $⌈.⌉$ is a ceiling function. The global probability of false alarm, $Q_f$, and the global probability of detection, $Q_d$, at the central entity are computed using the generalized K-out-of N Rule.

The generalized K-out-of-N Rule provided in [26] is employed to compute the global probabilities of false alarm, $Q_f$, and the global probability of detection, $Q_d$, as below:

$$Q_f=\sum _{i=K_2}^C\left\{\sum _{j=1}^{V_{K_2}^C}\left[\prod _{l=1}^{K_2}{P}_{f,j,l}\prod _{l=K_2+1}^C\left(1-P_{f,j,l}\right)\right]\right\},$$

(5)

$$Q_d=\sum _{i=K_2}^C\left\{\sum _{j=1}^{V_{K_2}^C}\left[\prod _{l=1}^{K_2}{P}_{d,j,l}\prod _{l=K_2+1}^C\left(1-P_{d,j,l}\right)\right]\right\},$$

(6)

where C is the number of participating members, i.e., CRs in a cluster or cluster heads in a CRN, $P_{f,j,l}$ and $P_{d,j,l}$ are the probability of false alarm and probability of detection of the i-th CR, $V_{K_2}^C$ = $C!/\left(K_2!\left(C-K_2\right)!\right)$, and ! denotes the factorial, $K_2=⌈\frac{C}{2}⌉$. Note that Equations (5) and (6) are used to find the global probability of detection and global probability of false alarm when the participating members have different, i.e., not equal, probabilities of detection and probabilities of false alarm.

Special case: if a group of CRs, i.e., a cluster of N CRs, are close to each other, they experience the same radio conditions, then it can assume that $P_{d1}=P_{d2}=\cdots =P_d$ and $P_{f1}=P_{f2}=\cdots =P_f$, i.e., the probability of detection and the probability of false alarm of all CRs in the cluster are the same [24], then Equations (5) and (6) are simplified as

$$Q_f=\sum _{i=K}^N\left(\genfrac{}{}{0pt}{}{N}{i}\right)P_f^i{[1-P_f]}^{N-i},$$

(7)

$$Q_d=\sum _{i=K}^N\left(\genfrac{}{}{0pt}{}{N}{i}\right)P_d^i{[1-P_d]}^{N-i},$$

(8)

where $K=⌈\frac{N}{2}⌉$ and N is the number of the CRs in the cluster.

2.2.2. Two-Bit Softened Hard Scheme

Unlike the one-bit scheme where the local decision is made using one threshold, the two-bit hard scheme employs three thresholds (${\lambda }_1$, ${\lambda }_2$, ${\lambda }_3$), to make the local decision as shown in Figure 2. The whole range of energy is divided into four regions where each region is allocated with a different weight value due to the distinction in the observed energies. Thus, each CR needs to exchange two bits to identify which region its observed energy belongs to. The detection criteria depends on the weighted summation given by $S_C={\sum }_{b=0}^3{w}_b{S}_b$ where $S_b$ indicates the number of observed energies falling in region b and the weight values assigned to each region are given by ($w_0=0,w_1=1,w_3=L,w_4=L^2$); where L is a design parameter to be optimized. The weighted summation is compared to a predefined threshold, $S_C=L^2$. The channel is detected as occupied if $S_C\ge L^2$; otherwise, it is detected as idle.

In the two-bit softened hard scheme, the three thresholds (${\lambda }_1$, ${\lambda }_2$, ${\lambda }_3$) which denote three local probabilities of false alarm ($P_{f1},P_{f2},P_{f3}$), respectively, are determined to satisfy a specific $Q_f$. To meet the required $Q_f$, $S_C$ should be less than $L^2$ which can be interpreted in Equation (9) where $B=L^2-1$ and $D_b=min\left\{⌊\frac{L^2-1-b{w}_1}{w_2-w_1}⌋,b\right\}$ with $⌊.⌋$ denoting the floor function.

Two design parameters ${\beta }_1$ and ${\beta }_2$ are defined as ${\beta }_1=\frac{P_{f2}}{P_{f1}}$, ${\beta }_2=\frac{P_{f3}}{P_{f2}}$. An exhaustive search is employed to determine L, ${\beta }_1$ and ${\beta }_2$. Thereafter, the value of $\rho$ which is given by $\rho =\frac{P_{f1}}{1-P_{f1}}$ is determined using Equation (10).

The total probability of detection is obtained likewise as in Equation (11); the values of L, ${\beta }_1$ and ${\beta }_2$ are numerically calculated to maximize the average $Q_d$ while meeting the required $Q_f$.

When S, $Q_f$, ${\beta }_1$, ${\beta }_2$ and $\rho$ are known, the values of $P_{f1}$, $P_{f2}$ and $P_{f3}$ can be obtained while ${\lambda }_1$, ${\lambda }_2$ and ${\lambda }_3$ can be determined in a subsequent manner from Equation (1). Then, $P_{d_1}$, $P_{d_2}$ and $P_{d_3}$ of the Rayleigh fading channel can be obtained from Equation (4).

$$1-Q_f=A_1\sum _{b=0}^B\left(\genfrac{}{}{0pt}{}{S}{b}\right){(1-P_{f_1})}^{S-b},$$

(9)

$$\left(1-Q_f\right){\left(1+\rho \right)}^S=A_2\sum _{b=0}^B\left(\genfrac{}{}{0pt}{}{S}{b}\right),$$

(10)

$$Q_d=1-A_3\sum _{b=0}^B\left(\genfrac{}{}{0pt}{}{S}{b}\right){(1-P_{d_1})}^{S-b},$$

(11)

where $A_1={\sum }_{d=0}^{D_b}\left(\genfrac{}{}{0pt}{}{b}{d}\right){\left(P_{f_1}-P_{f_2}\right)}^{b-d}{\left(P_{f_2}-P_{f_3}\right)}^j$, $A_2={\sum }_{d=0}^{D_b}\left(\genfrac{}{}{0pt}{}{b}{d}\right)\times {\left(1-{\beta }_1\right)}^{b-d}{\left({\beta }_1-{\beta }_1{\beta }_2\right)}^d{\rho }^d$, and $A_3={\sum }_{d=0}^{D_b}\left(\genfrac{}{}{0pt}{}{b}{d}\right){\left(P_{d_1}-P_{d_2}\right)}^{b-d}{\left(P_{d_2}-P_{d_3}\right)}^d$.

3. System Model

Assume a cognitive radio network (CRN) with a single PU and N multiple CRs as depicted in Figure 3. All CRs are assumed to use energy detector as a spectrum sensing approach. The CRs are grouped into multiple clusters according to their geographical locations. A central entity, i.e., FC, is coordinates the CRN, controls the transmission of the CRs, and selects a cluster head (CH) for each cluster in the CRN. Based on the largest reporting gain in the cluster, the CH is selected. Other CRs in the cluster are called cluster members (CMs). As aforementioned, the CRs within the cluster are assumed to experience the same radio conditions, i.e., have identical average SNR of the received PU signal since they are located near each other and the distance between them is much smaller compared with their average distance to the PU. The CMs forward their local observations to the CH through a error-free reporting channel, i.e., perfect reporting channel, because all CRs in the cluster are geographically closed to each other.

This system has two fusion levels, a cluster level and a CRN level. In a cluster level, a CH collects local observations from its CMs, combines them with a certain fusion rule to formulate a cluster decision, and forwards the cluster decision to the FC through a reporting channel. The CRN level consists of multiple clusters. In a CRN level, FC collects clusters’ decisions, fuses them to extract the global decision about the existence of the PU, and then disseminates back the global decision to the CHs. It is noteworthy that reporting channel between FC and CHs is assumed imperfect because clusters are far apart from the FC, and each cluster has different and independent average SNR of the PU signal due to its geographical location.

It is assumed that the clusters are located at different distances from the PU and that the PU SNR at the cluster level is defined as [27]:

$${\gamma }_c=\frac{P_{PU}}{{\sigma }^2}\frac{\delta }{R^{\alpha }}$$

(12)

where $\delta$ is the path loss constant, $\alpha$ is the path loss exponent, $P_{PU}$ is the transmit power of the PU, ${\sigma }^2$ is the noise variance and R is the average distance between the cluster center and the PU.

4. The Proposed Combination Algorithms

The paper proposes three different combination algorithms, namely, simple, modified and adaptive. The first two combination algorithms employ a fixed threshold strategy, while the latter employs adaptive threshold strategy. Details are provided below.

4.1. Simple Combined Algorithm

In this case, a fixed threshold is employed to determine whether the CHs uses one-bit fusion rule or two-bit fusion rule. The threshold, ${\overline{\gamma }}_c$, is the mean value of all participating clusters’ SNRs. It is assumed that there are C participating cluster in the CRN. At cluster level, as a first step, each CH estimates its SNR and forwards it to the FC to compute the threshold, ${\overline{\gamma }}_c$. Second step, each CH compares its SNR, ${\gamma }_c\left(i\right)$, with the threshold; if its greater than it, then the CH will employ one-bit fusion rule and its probability of detection is computed using Equation (8). Otherwise, the CH will employ two-bit fusion rule and its probability of detection is computed using Equation (11). Finally, at CRN level, the global probability of detection is computed using the generalized formula as in Equation (6), since probabilities of detection of the participating clusters are not equal. Algorithm 1 shows the mechanism of the simple combined fusion algorithm.

Algorithm 1 Simple Combined Algorithm

1: The FC collects the location information of each SU and determines the CHs based on the maximum reporting channel gain. 2: Each SU forwards its local observations and its estimated SNR to its CH. 3: Each CH sends its average SNR, ${\gamma }_c\left(i\right)$, to the FC to find the average SNR, ${\overline{\gamma }}_c$, of all the clusters. 4: for$i=1:C$, 5: $Q_d$ is computed using Equation (8), if ${\gamma }_c\left(i\right)>{\overline{\gamma }}_c$. (i.e., one-bit hard scheme) Otherwise $Q_d$ is calculated using Equation (11). (i.e., two-bit softened hard scheme) 6: end 7: The global probability of detection is made at the FC using Equation (6).

4.2. Modified Combined Algorithm

Similar to Algorithm 1, every CH has to forward its SNR, then FC computes the threshold ${\overline{\gamma }}_c$. Based on the threshold, each CH determines its fusion rule and the probability of detection. However, we modify Algorithm 1 by adding another threshold, i.e., eligibility threshold, to the simple combined algorithm. The eligibility threshold is added to improve the detection performance by involving only the clusters with high probability of detection in a final decision making at the CRN level. In other words, the clusters with low probability of detection will be excluded from decision making at the CRN level, therefore, reporting overhead will be significantly reduced.

The eligibility threshold is determined as the minimum accepted probability of detection, $Q_D=0.5$. The eligible clusters have probability of detection, $Q_d$, greater than the eligibility threshold. Then, eligible clusters will forward their observations to the FC, while others refrain from forwarding their observations. Note that in this algorithm, we employ two fixed thresholds. Algorithm 2 illustrates the modified combined fusion algorithm.

Algorithm 2 Modified Combined Algorithm

1: Find the estimation of SNR of each cluster (${\gamma }_c\left(i\right)$) and compute (${\overline{\gamma }}_c$) 2: Specify$Q_D$. 3: for$i=1:C$, 4: if${\gamma }_c\left(i\right)>{\overline{\gamma }}_c$ 5: compute$Q_d\left(i\right)$ using Equation (6) 6: else if 7: compute$Q_d\left(i\right)$ using Equation (11) 8: end for 9: if$Q_d\left(i\right)>Q_D$ 10: The $i^{th}$ CH forwards its decision to the FC 11: else 12: continue 13: end if 14: The global decision is made at the FC using Equation (6) for the eligible clusters .

4.3. Adaptive Combined Algorithm

Unlike Algorithms 1 and 2, a variable eligibility threshold, $\phi$, will be used in this case. An iterative algorithm is devised to update the value of $\phi$. The eligibility threshold, $\phi$, varies to minimize the total detection error rate denoted by $Q_{ER}$ and is computed as follows

$$Q_{ER}=P\left(H_0\right)Q_f+P\left(H_1\right)\left(1-Q_d\right)$$

(13)

where $P\left(H_0\right)$ and $P\left(H_1\right)$ are the probabilities of the PU being absent and present, respectively.

Algorithm 3 Adaptive Combined Scheme

1: SET${\overline{Q}}_{fc}$ and $\phi$ 2: Let$\mathit{Q}\leftarrow ⌀$ 3: Compute$Q_{dc}\left(i\right)$ for all clusters in the system, where $i=1,2,\cdots ,C$. 4: Let$\mathbf{U}=\left[Q_{dc}\left(1\right),\cdots ,Q_{dc}\left(C\right)\right]$ 5: Sort the rows of $\mathbf{U}$ in a descending order. 6: for$i=1:C$ 7: $I=U(i,:)$ 8: for$j=1:length\left(I\right)$ 9: if$I\left(j\right)>\phi$ 10: $\mathit{Q}=I\left(j\right)$ 11: else 12: $\phi =I\left(j\right)$ 13: break 14: end 15: end 16: Compute the global probability of false alarm of the CRN using Equation (5) 17: if$Q_f\left(i\right)<{\overline{Q}}_{fc}$ 18: Compute the global probability of detection of the CRN using Equation (6) 19: else 20: $\mathit{Q}=\left[\mathit{Q}\phi \right]$ 21: Compute the global probability of detection of the CRN using Equation (6) 22: Compute the global probability of false alarm of the CRN using Equation (5) 23: end 24: end

The first step of the adaptive combined algorithm is to set the initial value of the maximum allowable global probability of false alarm, ${\overline{Q}}_{fc}$, and the adaptive threshold $\phi$. The ${\overline{Q}}_{fc}$ is set as either $0.05$ or $0.005$ which the maximum expected probability of false alarm over a cluster, while the adaptive threshold, $\phi$, is set as the average of probabilities of all clusters in the CRN, when all clusters employ one-bit fusion rule. In other words, each cluster computes its probability of detection using Equation (8).

The second step is to update $\phi$ through an iterative algorithm to ensure improving $Q_d$ and minimizing $Q_{ER}$, simultaneously. This is achieved by sorting the probabilities of detection of the clusters and then comparing them to $\phi$. The $\phi$ is updated to exclude clusters with a low probability of detection. Furthermore, to guarantee attaining minimum error detection for involved clusters, each cluster computes its probability of false alarm using Equation (7) then compares it by the ${\overline{Q}}_{fc}$. The i-th cluster will be excluded if $Q_f\left(i\right)\ge {\overline{Q}}_{fc}$.

As a conclusion, the threshold, $\phi$, in the adaptive combined algorithm varies adaptively to increase total probability of detection, i.e., detection performance, which results in decreasing the total detection error rate, $Q_{ER}$. Algorithm 3 illustrates the mechanism of the adaptive combined fusion algorithm.

5. Reporting Overhead Analysis

The closed-form expressions for the number reporting bits over a reporting channel for four different fusion schemes are demonstrated in

Table 1. Reporting overhead analysis for four different fusion schemes.

Fusion Scheme	Number of Bits at the Cluster Level	Number of Bits at the FC Level
One-bit hard	$(S-1)C$	C
Two-bit softened hard	$2(S-1)C$	C
Simple combined	$2(S-1)D_1+(S-1)(C-D_1)$	C
Modified combined	$2(S-1)D_3+(S-1)D_4$	$D_2$

, the analysis includes one-bit hard, two-bit softened hard, simple combined, and modified combined fusion algorithms. The adaptive combined algorithm is not included because the number of reporting bits varies with the variation of the eligibility threshold. Therefore, close form expression for this algorithm cannot be extracted. The communications between the CHs and their members or the FC incur reporting overhead, i.e., collaboration cost. The reporting overhead, H is computed as a product of the number of reporting bit, N and the bandwidth, B, i.e., $H=NB$.

Note that $D_1$ is the number of the clusters that employ two-bit fusion, $D_2$ is the number of the eligible clusters when using simple combined algorithm. $D_3$ is the number of the clusters that employ two-bit fusion and $D_4$ is the number of the clusters that employ one-bit fusion when using modified combined algorithm. Recalling that C is the number of the clusters and S is the number of the users in the cluster.

On the other hand, the power consumption also adds an extra overhead. The power consumption of a scheme reflects the energy efficiency of that scheme. The power consumption of N CRs in a CRN is computed as a sum of sensing power, $P_1$, and reporting power, $P_2$. The $P_1$ is computed as $P_1=NPs$, while the $P_2$ is computed as, $P_2=N_r{P}_t$, where $N_r$ is the total number of reporting CRs in a CRN, $P_s$ is the power consumed by a CR to detect a PU, and $P_t$ is the transmission power of a CR.

6. Simulation Results

MATLAB simulation environment is employed to simulate different scenarios to investigate the detection performance of different fusion schemes versus factors, such as number of sensing samples, M, fusion rule parameter, K, and the number of users per cluster, S. The simulation parameters are selected as M = 10, ${\overline{Q}}_{fc}$ =0.05, S = 4 CRs, C = 5 clusters, L = 2, $\alpha$ = 3, $\delta$ = 1, $P\left(H_0\right)$ = $P\left(H_1\right)$ = 0.5, $Q_D$ = 0.5, $P_s$ = 0.1 mW and $P_r$ = 0.5 mW.

For simplicity, it is assumed that there are five clusters with the same number of CRs. Moreover, it is assumed that all clusters experience Rayleigh fading channel. It is worth mentioning that the values of the two-bit softened hard scheme (i.e., ${\beta }_1$ and ${\beta }_2$) are determined off line using exhaustive search and are stored in a look up table to reduce the computational complexity.

A comparison in a total probability of detection considering a different number of sensing samples between the four fusion schemes, namely, one-bit, two-bit, simple combined, and modified combined schemes, under Rayleigh fading channel is demonstrated in Figure 4. The figure shows that the modified combined algorithm outperforms the three other fusion schemes, since this algorithm ignores the clusters with low probability of detection. Moreover, it is noticed that the simple combined fusion algorithm only outperforms the one-bit fusion scheme, the improvement comes due to converting the fusion rule of some cluster from one-bit to two-bit fusion scheme [24].

For further comparisons, the impact of varying the number of CRs in each cluster on the total probability of detection with different values of fusion rule parameter K attained by the schemes is considered. Figure 5 provides a comparison between the four fusion schemes in terms of probability of detection considering the impact of selecting different values of fusion rule factor, K. The figure also shows the superiority of the modified combined algorithm over the three other schemes. It also shows that the detection performance improves as the number of CRs increases which increases the spatial diversity.

Figure 6 investigates the impact of increasing the number of users, i.e., CRs, in a cluster on the total probability of detection for the four above-mentioned schemes and the weighted fusion algorithm [16]. The figure shows that the modified combined algorithm outperforms the weighted fusion algorithm as the number of CRs in a cluster increases, this is because the modified combined algorithm ignores the unreliable clusters which have probability of detection less the eligibility threshold, i.e., $Q_{dc\left(i\right)}<Q_D$, while the weighted fusion algorithm includes all clusters with their weights which reduces the total probability of detection.

Figure 7 displays the consumed power of the four schemes in three cases. Case 1 represents a CRN with five clusters, each cluster with three CRs, case 2 represents a CRN with five clusters, each cluster has four CRs, while case 3 represents a CRN with five clusters, each cluster has five CRs. The figure reflects the energy efficiency of the modified combined scheme, where modified combined scheme consumes less power compared to the two-bit scheme in all three cases. Furthermore, the figure shows that two-bit fusion rule always consumes more power compared to the three other schemes, since the two-bit scheme reports double the bits that required by the one-bit scheme. Moreover, it can be noticed that simple modified scheme outperforms two-bit scheme where it consumes less power when compared to two-bit scheme. Quantitatively, Figure 7 shows that the modified combined scheme can save about 32–34$\%$ of the power compared to two-bit softened hard scheme, while the simple combined scheme can save about 12–22$\%$ of the power compared to two-bit softened hard scheme in the three cases.

From reporting overhead perspective,

Table 2. Reporting overhead analysis for five clusters, each with four CRs.

Fusion Scheme	Number of Bits at the Cluster Level	Number of Bits at the FC Level	Total Number of Bits	Total Reporting Overhead
One-bit	15	5	20	20 B
Two-bit	30	5	35	35 B
Simple combined	24	5	29	29 B
Modified combined	18	4	22	22 B

compares the incurred reporting overheads for the four fusion schemes. The table shows that modified combined algorithm incurs less reporting overhead compared with simple combined and two-bit fusion schemes, since the modified combined algorithm considers only the eligible clusters to share in making final decision about the existence of the PU which significantly reduces the number of reporting bits transmitting over the reporting channel. Furthermore, the table shows that one-bit fusion scheme incur less number of reporting overhead than the modified combined fusion algorithm by about $9\%$, however, the latter fusion algorithm significantly outperforms the one-bit in the detection performance in terms of total probability of detection as shown in Figure 4 and Figure 5. Moreover, the modified combined fusion algorithm incurs less reporting overhead between the CHs and the FC compared with the three other fusion schemes. Quantitatively, Table 2 shows that simple combined scheme and modified combined scheme can save 17% and 37% of the reporting compared with Two-bit scheme, respectively.

Figure 8 compares the probability of detection, i.e., detection performance, for different values of SNR for one-bit, two-bit, simple combined, and adaptive combined schemes under Rayleigh fading channel when the maximum allowable probability of false alarm constraint of $Q_f=\{0.05,0.005\}$. The figure shows that adaptive combined algorithm outperforms all other fusion schemes for the total SNR range under both values of constraints because the eligibility threshold is varying such that the total probability of detection would increase. Moreover, the figure ensures that $Q_d$ increases as SNR increases as proven in [10].

For comprehensive comparisons, a weighted fusion algorithm [28] is considered to investigate the detection performance of all schemes mentioned in the previous cases. In the weighted fusion algorithm, each cluster is assigned with a weight value proportional to its SNR, the weight of the i-th cluster, $w_i$ is provided as, $w_i=\frac{{\overline{\gamma }}_i}{max\left(\overline{\gamma }\right)}$), where ${\overline{\gamma }}_i$ is the average SNR over the i-th cluster, while $max\left(\overline{\gamma }\right)$ is the largest average SNRs among all clusters in the systems.

The comparison between all above-mentioned schemes involves obtaining the total probability of detection and the incurred total detection error rate as performance metrics which are displayed in Figure 9 and Figure 10, respectively.

The impact of increasing SNR on the total probability of detection attained by different fusion scheme is depicted in Figure 9. The figure shows that adaptive combined algorithm outperforms the four other schemes over the SNR range of $\gamma \in \left[-4,2\right]$, since the eligibility threshold of this algorithm adaptively changes to improve the total probability of detection. Furthermore, the figure shows that the adaptive combined algorithm and the weighted fusion algorithm have almost the same total probability of detection for SNR higher than 2 dB, since probability of detection significantly increases by increasing the SNR.

Moreover, the impact of SNR on the total detection error rate for different schemes is investigated in Figure 10. The figure shows that adaptive combined algorithm incurs the least total probability of error, $Q_{ER}$ over the SNR range of $\gamma \in \left[-4,2\right]$. This reduction in $Q_{ER}$ comes as a result of increasing the total probability of detection of the algorithm. The figure also shows that both adaptive combined algorithm and weighted fusion algorithm have almost the same detection error rate in higher SNR range, because the attained total probability of detection of both schemes are almost the same over high SNR range as shown in Figure 9.

7. Conclusions

This paper has proposed fusion combination algorithms that improve the detection performance by increasing the attained total probability of detection and reducing the incurred total detection error rate. Three proposed combination algorithms have been discussed and implemented. The proposed algorithms have employed different threshold strategies by selecting different eligibility threshold. A comparison between the proposed algorithms and some existing schemes has been considered to evaluate their detection performance under Rayleigh fading channel condition. Moreover, the detection performance of the algorithms has been examined to investigate the impact of increasing number of sensing samples, the number of users in a cluster and the ambient radio condition, i.e., SNR. Moreover, simulation results have shown that modified combined algorithm significantly reduces the incurred reporting overhead and power consumption. Furthermore, the simulation results have shown that there is a considerable power saving by the modified scheme compared to the two bit scheme , e.g., 32–34% for the three considered cases. Also, a remarkable bandwidth saving can be achieve by the modified combined scheme compared to the two-bit scheme , e.g., 37% for case 2. In addition, simulation results have shown the effectiveness of adaptive combined algorithm over the two other proposed algorithms as well as the conventional schemes, i.e., one-bit hard and two-bit softened hard.

References