# Mobility-Enhanced Reliable Geographical Forwarding in Cognitive Radio Sensor Networks
## 4 MROR System and Network Model
### Mobility-Enhanced Channel Availability Modeling
#### 4.2.1 PU Protection  
To ensure protection of PU communication, a primary transmitter keep-out radius is enforced by the regulatory body. Under the interference temperature limits (ITL), this distance is the minimum allowed distance between the transmitting PU and an SU under which an SU is not allowed to transmit. \[Z_{e,i}=\inf\left\{d\in\mathbb{Z}\left|\sum\limits_{\forall n}I\left(\delta_{s,i},d\right)\leq ITL\right.\right\} \tag{4}\]  
where \(\sum\limits_{\forall n}I\left(\delta_{s,i},d\right)\) represents the average interference generated by all of the \(n\) SUs on a primary receiver located at the edge of the coverage area of the primary transmitter on channel \(i\); while \(\delta_{s,i}\) represents the SUs density on the channel \(i\). Accordingly, cumulative interference from SU to a primary receiver located at a distance \(Z_{o}\) (_i.e._, located at the edge of the coverage of the primary transmitter) can be bounded as [26]:  
\[I_{i}^{U}\left(\delta_{s,i},Z_{e,i}\right)=\frac{2\pi P_{o}d_{o}^{\alpha}\delta _{s,i}}{\alpha-2}\left(Z_{e,i}-Z_{o}\right)^{2-\alpha} \tag{5}\]  
where \(P_{o}\) represents the SU's transmission power, \(d_{o}\) is the reference distance, \(\alpha\) represents the path-loss exponential, \(Z_{o}\) the PU's transmission radius, \(Z_{e,i}\) the base station's keep-out radius and \(\delta_{s,i}\) is the average SU density on channel \(i\). Thus, for Equation (5), we can define the primary transmitters' keep-out radius necessary to achieve the interference constraint, \(I_{i}^{U}\leq ITL\), on channel \(i\) as:  
\[Z_{e,i}^{*}\left(\delta_{s,i}\right)=\left[\left(\frac{\alpha-2}{2\pi P_{o}d_{ o}^{\alpha}\delta_{s,i}}\cdot ITL\right)^{\frac{1}{2-\alpha}}\right]^{+}+Z_{o} \tag{6}\]  
From Equation (6), it can be observed that, for channel \(i\), the keep-out radius increase with the PUs' density. This basically means that, as more SUs access channel \(i\), the keep-out radius has to be accordingly expanded to keep up with the ITL constraint. Since the formulation in Equation (6) is for a scenario wherein the PUs are stationary, it might not represent sufficient protection for the PU transmission in the mobile scenario, as the rate at which new nodes enter this region might increase depending on the speed of the SUs. Thus, this radius has to be adequately expanded to ensure PU protection in the mobile scenario. To achieve this, an addition protection layer referred to as the mobility-induced guard (mguard) distance, \(\ell_{i}\), is introduced. When considered together with the ITL, we come up with a new mobility-induced protection (MIP) region, \(\Implement\), for the primary transmitter. Thereby, if \(P_{i}\) represents a set of transmitting PUs on channel \(i\), the MIP region for a transmitting PU \(\xi\in P_{i}\), located at \(x_{i,\xi},y_{i,\xi}\), will represent the unit disc around \(\xi\). \[\Implement_{i,\xi}=\left\{\left(x,y\right)\in\mathbb{Z}^{2}\left|\left|\left(x_ {i,\xi},y_{i,\xi}\right)-\left(x,y\right)\right.\right|\leq Z_{e,i}+\ell_{i} \right.\right\} \tag{7}\]  
According to Equation (7), when an SU moves into any MIP region of an active PU, it can only initiate route formation if it is the source, and it can also compete in forwarding data packets if its instantaneous channel condition meets the session requirements of the active route.