## 7 System Performance Optimization
### System Optimization Model  
We know that when two wireless transmitters are in a certain range of distance, if they work on the adjacent channels, there will exist channel interference between them, and we call the two wireless transmitters neighbors. The distance can be called \(D_{neighbor}\).; However, when the distance between them is greater than \(D_{neighbor}\), the channel interference will not occur even when they work on adjacent channels.  
Based on the analysis above, the strength of channel interference can be mapped into a function f(d,channel), and an optimization model is built for the system. As shown in Figure 4, the channel interference can be mapped into two vectors, min vector and max vector, where min vector represents the channel interference between the safe wireless transmitter and the normal public wireless transmitters, while max vector represents the channel interference between the safe wireless transmitter and the target public APs.  
In order not to interfere with the normal public wireless transmitters, min vector will give a proper position where the safe wireless transmitter is not the neighbor of the normal wireless transmitters, while max vector will give a proper channel.  
min vector  
\[f(d_{N_{i}},channel)+...+f(d_{N_{i}},channel)+...+f(d_{N_{i}},channel) \tag{1}\]  
max vector  
\[f(d_{A_{1}},channel)+...+f(d_{A_{j}},channel)+...+f(d_{A_{m}},channel) \tag{2}\]  
under the following constraints:  
(i) Distance constraint:  
\[max\ d_{A_{i}}\leq D_{neighbor}\leq d_{N_{i}}\]  
(ii) Channel constraints:  
\[packet\ loss\ rate_{CSI\ values}\geq\delta\]  
\[packet\ loss\ rate_{normal\ QoS}\leq\gamma\]  
where \(d_{N_{i}}\) represents the distance between the safe wireless transmitter and normal public wireless transmitters, while \(n\) represents the number of normal wireless transmitters in the public place; \(d_{A_{j}}\) represents the distance between the safe wireless transmitter and the target public APs, while \(m\) represents the number of target public APs; \(D_{neighbor}\) represents the distance at which the two wireless transmitters can be neighbors.  
Figure 4: Interference vector.  
The distance constraints can be interpreted as follows: in order to interfere with the target public APs, the distance \(d_{A_{i}}\) should be shorter than \(D_{neighbor}\), so that when they work on adjacent channels, there will exist channel interference between the safe wireless transmitter and the target public APs. In order not to interfere with the normal public wireless transmitters, the distance \(d_{N_{i}}\) should be large than \(D_{neighbor}\), so that even when they work on adjacent channels, there will not exist channel interference between the safe wireless transmitters and normal public wireless transmitters.  
The interpretation of the channel constraints is as follows: in order to interfere with the CSI measurements at the receiver end so that the attacker cannot recover the input sensitive information, the packet loss rate for CSI measurements needs to be larger than the threshold \(\delta\); in order not to affect the normal network service, the packet loss rate of QoS should be smaller than the threshold \(\gamma\).