# Combined Fusion Rules in Cognitive Radio Networks Using Different Threshold Strategies
## 1 Introduction
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.