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, eigenvaluebased 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, ClusterBased 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 reductionoriented 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 metricbased schemes which balance the tradeoff 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 metricbased 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 twobit decision and onebit 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 onebit or twobit decision rule to the Fusion Center (FC). The data reconstruction module is implemented using a multibit 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 quantizationbased multibit data soft fusion rule instead of forwarding local onebit 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 nonuniform quantized data fusion (NQDF) rule to minimize the reporting overhead for EDbased 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 twobit and onebit 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 onebit rule or twobit rule as illustrated in Algorithm 1. The second strategy is performancebased 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., onebit, and softenedhard decision, i.e., twobit, 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 onebit hard decision rule over the hierarchical structure of the clusters, while our work in [
16] proposes a weighting strategy to combine twobit and onebit 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.
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 errorfree 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]:
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 onebit fusion rule or twobit 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 onebit fusion rule and its probability of detection is computed using Equation (
8). Otherwise, the CH will employ twobit 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., onebit hard scheme) Otherwise ${Q}_{d}$ is calculated using Equation ( 11). (i.e., twobit 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
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$\mathit{Q}\leftarrow \u2300$  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:
$\mathit{Q}=\left[\mathit{Q}\phantom{\rule{4pt}{0ex}}\phi \right]$  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 onebit 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
ith 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 closedform expressions for the number reporting bits over a reporting channel for four different fusion schemes are demonstrated in
Table 1, the analysis includes onebit hard, twobit 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 twobit 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 twobit fusion and ${D}_{4}$ is the number of the clusters that employ onebit 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 twobit 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, onebit, twobit, 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 onebit fusion scheme, the improvement comes due to converting the fusion rule of some cluster from onebit to twobit 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 abovementioned 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 twobit scheme in all three cases. Furthermore, the figure shows that twobit fusion rule always consumes more power compared to the three other schemes, since the twobit scheme reports double the bits that required by the onebit scheme. Moreover, it can be noticed that simple modified scheme outperforms twobit scheme where it consumes less power when compared to twobit scheme. Quantitatively,
Figure 7 shows that the modified combined scheme can save about 32–34
$\%$ of the power compared to twobit softened hard scheme, while the simple combined scheme can save about 12–22
$\%$ of the power compared to twobit softened hard scheme in the three cases.
From reporting overhead perspective,
Table 2 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 twobit 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 onebit 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 onebit 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 Twobit scheme, respectively.
Figure 8 compares the probability of detection, i.e., detection performance, for different values of SNR for onebit, twobit, 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
ith 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
ith cluster, while
$max\left(\overline{\gamma}\right)$ is the largest average SNRs among all clusters in the systems.
The comparison between all abovementioned 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.