# Fast and Robust Asynchronous Rendezvous Scheme for Cognitive Radio Networks
## 5 Performance Evaluation  
The considered network consists of two SUs and one channel-detection jammer that has similar functions as a legitimate user. Each SU is assumed to be equipped with a single antenna and operates in half-duplex mode, hence, no terminal can transmit and receive data simultaneously. However, the jammer can listen on two channels at the same time by using two transceivers to show how to quickly detect CH sequences of SUs. I implemented CH sequences for the sender and the receiver according to the considered rendezvous algorithms and the CDJA model by using MATLAB [10], and computed the TTR values and the rendezvous probabilities for the performance evaluation. I first evaluated the effect of the CDJA model on the EJS rendezvous method since the EJS system is an advanced system of the JS system. I then implemented the symmetric and asymmetric FRARS schemes to show that it is more resistant to jamming attacks than EJS systems. First, in a symmetric scenario, the mean time to rendezvous (TTR) without considering a jamming attack is compared for both EJS and FRARS schemes. Figure 6 shows the mean TTR for both EJS and FRARS schemes when the \(M\) increases from 4 to 100. For each available channel case, I repeated the above process 1000 times to calculate the average TTR. The starting position of the receiver can be any time slot of the sender's sequence in the both EJS and FRARS schemes due to no time synchronization. In both schemes, as the number of available channels increases, the average TTR tends to gradually increase. The TTR result of symmetric EJS is about half value of \(M\) and is slightly better than that of the symmetric FRARS. The results are consistent with the upper-bound EITR of the symmetric EJS scheme (i.e., \(\frac{3}{2}P+3\)) [9] and the EITR of the FRARS scheme (i.e., \(\frac{3}{4}M+\frac{1}{4M}\)) respectively. Next, I compare the rendezvous probabilities for symmetric EJS and FRARS schemes under jamming attacks using the CDJA model. For the EJS scheme, a single jammer can fully detect the CH sequence of a sender within the \(P\) time slots and jams all remaining time slots; thus, I use two jammers for the FRARS scheme in this experiment. As shown in Figure 7, the rendezvous probability of  
Figure 6: The average Time To Rendezvous (TTR) results for the symmetric FRARS and EJS schemes with \(M=[4,\cdots,100]\). symmetric EJS scheme is significantly reduced due to the CDJA attack and is less than 10%. However, the probability of a rendezvous in a symmetric FRARS system is almost stable and close to 100%. For an asymmetric scenario, in Figure 8, I show the average TTR of the asymmetric FRARS as well as the theoretical EUTR of FRARS mentioned in Section 4.2. The number of available channels of the sender or receiver is denoted by \(m_{i}\) and is half of the \(M\) (i.e., \(|m_{i}|/|M|=0.5\)) and \(|G|=1\) for various \(M=\{10,20,\cdots,90,100\}\). Figure 8 shows that the average TTR values for the asymmetric FRARS are not significantly different from the theoretical EUTR \(\frac{(2M-1)(|m_{2}|-G)}{2M-1}+\left(\frac{2(M-|m_{1}|)-1}{2M-1}-\frac{|m_{1}| }{G}+(1-\frac{2(M-|m_{1}|)-1}{2M-1})\cdot(\frac{3}{4}M+\frac{1}{4M})\right)\). As I have seen in the above symmetric scenarios, I now firstly analyze the asymmetric EJS and FRARS schemes by comparing the mean TTRs without a jamming attack. In addition, I then compare the rendezvous probability for both the asymmetric EJS and FRARS using the CDJA model. Figure 9 shows the average TTRs for the asymmetric EJS and FRARS schemes when the \(M\) is  
Figure 8: The average TTR and the theoretical EUTR for the asymmetric FRARS scheme with \(|m_{1}|=|m_{2}|=|M|/2\), \(M=[4,\cdots,100]\), and \(G=1\). Figure 7: The probability of rendezvous for the symmetric EJS and FRARS schemes under CDJA attacks with \(M=[4,\cdots,100]\). \(\{10,20,\cdots,90,100\}\), \(|m_{1}|=|m_{2}|=|M|/2\), and \(G\) are \(1\) and \(10\). When the \(G\) is \(1\), the average TTR of the asymmetric FRARS is about half of the asymmetric EJS algorithm.