# SACRB-MAC: A High-Capacity MAC Protocol for Cognitive Radio Sensor Networks in Smart Grid
## 4 Results and Discussion  
In this section, the performances of SACRB-MAC on a single hop and multiple hops in smart grid AMI networks will be evaluated. A MATLAB based simulation is performed to verify the analytical models. Specifically, a square region of side 1200 m with 16 PU existing is considered. We assume that the cognitive radio sensors with transmission the radius of 150 meter are Poisson distributed in the whole region with a mean density, which is shown in Figure 3. Without loss of generality, we assume that Routing Protocol for Low Power and Lossy Networks (RPL) is adopted at the Network layer. The parameters of the simulation are as shown in Table 1. In addition, we also perform a receiver-based MAC protocol (CRB-MAC) and a sender-based MAC protocol (1-hopMAC [28]) under the cognitive radio environment (CSB-MAC) for comparison. First, we evaluate the performance of delay. The single hop delay against bit error rate (BER) is evaluated in Figure 4. The two receiver-based protocols have better performance. This is because that the delay performance is mainly dependent on the number of retransmissions. Due to the receiver-based nature, SACRB-MAC and CRB-MAC have fewer retransmissions than CSB-MAC. Moreover, the delay performance has a saturation point when the retransmission count reaches the maximum. \begin{table}
\begin{tabular}{l c} \hline \hline
**Parameter** & **Value** \\ \hline Detection probability threshold (\(P_{d}^{j}\)) & 0.9 \\ Probability of false alarm (\(P_{f}\)) & 0.1 \\ Channel bandwidth & 2 MHz \\ PU received SNR (\(\gamma\)) & \(-15\) dB \\ Busy state parameter of PU (\(\mu_{ON}\)) & 2 \\ Idle state parameter of PU (\(\mu_{OFF}\)) & 3 \\ Maximum Interference Ratio (\(lR_{max}\)) & 0.25 \\ Spectrum sensing duration (\(T_{s}\)) & 20 ms \\ CR node transmission range & 150 m \\ Maximum transmitting power of each node (\(\mathcal{P}_{max}\)) & 30 dBm \\ Maximum allowed transmitting power of channels (\(\mathcal{P}_{j,i}^{an}\)) & 20–30 dBm \\ Checking interval (\(T_{CI}\)) & 144 ms \\ Preamble length (\(T_{pr}\)) & 144 ms \\ Transmission time of a data packet (\(T_{d}\)) & 4 ms \\ Transmission time of one micro-frame (\(T_{m}\)) & 40 μs \\ Transition time from sleep mode to active mode (\(\tau\)) & 88.4 μs \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation Configuration Parameters  
Figure 3: Sample simulated topology with Poisson distributed nodes (density = 400 nodes per square kilometers). The filled squares and dotted circles represent the location and coverage area of PU transmitters, respectively. In Figure 5, the performance of multi-hop delay is evaluated. We note that the end-to-end delay increases linearly as the number of hops increases. CRB-MAC and SACRB-MAC outperform CSB-MAC in the performance of end-to-end delay (in both low and high BER scenarios) due to fewer retransmissions. Besides, the performance of SACRB-MAC is near to that of CRB-MAC. In addition, the simulation results agree with the analytical ones. Next, we evaluate the capacity performance. The analytical and simulation results for the average capacity against network density are given in Figure 6. It is noted that the average capacity performance of SACRB-MAC initially increases and then decreases as the network density grows. This is because the probability of finding a receiver node with higher capacity grows with the network density. However, the probability of the preamble packet collision on the CCC increases as the network density increases. In high network density environments, the collision may cause average capacity degradation. In comparison, SACRB-MAC outperforms CRB-MAC and CSB-MAC obviously, because  
Figure 4: Single hop delay performance against bit error rate. Figure 5: Multi-hop delay performance against number of hops. of the adoption of the spectrum aggregation technique. Besides, the simulation result agrees with the analytical one. We evaluate the average capacity against the maximum transmitting power allowed in each channel.