# SACRB-MAC: A High-Capacity MAC Protocol for Cognitive Radio Sensor Networks in Smart Grid
## 2 SACRB-MAC Framework
### System Model  
We consider the AMI network structured by using cognitive radio-equipped sensors, which is shown as Figure 1. In this AMI network, multiple cognitive radio-enabled meters (located at the customer premises) transmit customer information to a Meter Data Management System (MDMS), which acts as a control center for the management of meter data in order to be used by different applications (for AMI details, see [23]). We assume that only one secondary network (_i.e._, the AMI network) exists in this region, and \(N\) stationary primary user (PU) transmitters (\(N\) spectrum band) exist with known locations and maximum coverage ranges. Moreover, \(M\) channels exist in each spectrum band. All CR meters adopt _Signal Interpretation before Fourier Transform_ (SIFT) and _Frequency-Aware OFDM_ (FA-OFDM) [24] techniques in radio transceivers and share a CCC for control information exchange, which is always available and reliable. Therefore, CR meters can aggregate channels from different spectrum bands and access these channels simultaneously for transmission [25]. Generally, the available spectrum for cognitive radio sensors is fragmented. The fragment size varies among different channels and bands. In order to detect these fragments, CR sensor nodes perform multiple channel spectrum sensing operation to the licensed spectrum bands. The status of channels are recorded in _Channel Status Table_ (CST), which is given by:  
Figure 1: The schematic of AMI networks. \[\mathbf{S}=\left[ \begin{array}{cccc}s_{11}&s_{12}&\cdots&s_{1M}\\ s_{21}&s_{22}&\cdots&s_{2M}\\ \vdots&\ddots&\vdots\\ s_{N1}&s_{N2}&\cdots&s_{NM}\end{array} \right]_{N\times M},\quad s_{jj}\in\{0,1\} \tag{1}\]  
where \(s_{j,i}\) denotes the status of the \(i\)-th channel of the \(j\)-th band and \(s_{j,j}=1\) indicates that the channel is available. The available channels for aggregation are selected based on CST. In addition, the CST is updated periodically based on the spectrum sensing results. In FA-OFDM, different coding and modulation schemes are adopted in the OFDM sub-band, and the coding and modulation scheme of each sub-band is dependent on its signal-to-noise ratio. Accordingly, the data are split and carried by different carriers, which may adopt different transmit rates and power. The schematic of the FA-OFDM-based PHY layer is shown as Figure 2.  
We also assume nonpreemptive CR node transmission when the wireless transceivers operates in transmission and reception mode. Even if the PU access the channel, the CR node will complete the current frame transmission and suspend the next frame data transmission. It is noted that PUs can access channels at any time instant, and their activities can be represented by a two-state independent and identically distributed random process, where the time of idle and busy periods is distributed with a mean of \(\frac{1}{\mu_{OFF}^{0}}\) and \(\frac{1}{\mu_{ON}^{0}}\), respectively. Let \(S_{idle}^{j,i}\) denote the state that the \(i^{th}\) channel in the \(j^{th}\) is idle with probability \(P_{idle}^{j,i}\). Similarly, \(S_{busy}^{j,i}\) denotes the state that PU is active in the \(i^{th}\) channel (busy) in the \(j^{th}\) with probability \(P_{busy}^{j,i}=\frac{\mu_{OFF}^{i}}{\mu_{ON}^{0}+\mu_{OFF}^{0}}\), and \(P_{idle}^{j,i}+P_{busy}^{j,i}=1\). The energy detection technique [26] is adopted here for PU detection, which is given by:  
\[Sensing\ Result=\left\{ \begin{array}{ccc}S_{busy}^{j,i}&\text{if}&E^{j,i} \geq\sigma\\ S_{idle}^{j,i}&\text{if}&E^{j,i}<\sigma\end{array} \right. \tag{2}\]  
In spectrum sensing, the detection probability (\(P_{d}\)) and the false alarm probability (\(P_{f}\)) are two metrics. High detection probability ensures good protection to PUs and low false alarm probability ensures efficient utilization of channels.