# Dynamic Carrier-Sense Threshold Selection for Improving Spatial Reuse in Dense Wireless LANs
## 3 Proposed Protocol
### Model-Based Dynamic CST Control  
In the model-based scheme, the CST required for protecting the transmission is calculated using a path loss model. For example, a log-distance path loss model can be used. Consider the scenario shown in Figure 2. AP1 is trying to send a packet to node S. The advertised CST should be low enough to block all nodes that can potentially interfere with the transmission at the receiver. A potential interferer is a node that can cause SNR at node S to drop below the required SNR to decode the packet. Suppose \(P_{1}\) is the received signal strength when the packet from AP1 arrives at node S, and \(SNR_{th}\) is the SNR required to reliably decode a packet. Also, suppose another node AP2 transmits concurrently with AP1, so its signal becomes an interference at node S, and the interference strength is \(P_{2}\). For the AP1's packet to be successfully decoded at node S, the following equation should hold. (We ignore the noise floor here, but the noise floor is considered in the simulations). Please note that all values are in dB scale. \[P_{1}-P_{2}\geq SNR_{th} \tag{2}\]  
We want to find the minimum interference level \(P_{2}\), which will make the packet reception fail at node S. We can calculate the minimum \(P_{2}\) that destroys the packet by converting the inequality in Equation (2) to equality. To calculate the minimum \(P_{2}\), AP1 must know \(P_{1}\), assuming \(SNR_{th}\) is fixed and known. There are two ways to obtain \(P_{1}\). First, node A constantly measures the RSSI of AP1, and send the information to AP1. Second, AP1 measures RSSI of node A whenever A transmits a packet, and assume that the links are symmetric and use that value as \(P_{1}\). Regardless of the methods, AP1 can obtain \(P_{1}\) and thus calculate \(P_{2}\) using Equation (3). \[P_{2}=P_{1}-SNR_{th} \tag{3}\]  
There are multiple positions of the interferer where the interference level at node S is \(P_{2}\). Among the positions, the farthest point from AP1 is at the opposite direction from node S. Let us assume there is an interferer AP2 placed at that position, as illustrated in Figure 2. Now, our goal is to calculate the RSSI of AP1, measured at AP2. We use the log-distance model, which calculates path loss according to the following equation. \[PL=PL_{0}+10\gamma\log_{10}\frac{d}{d_{0}}+X_{g} \tag{4}\]  
In the equation, \(PL\) is the path loss, \(PL_{0}\) is the reference path loss, \(d\) is the distance between the sender and the receiver, \(d_{0}\) is the reference distance, \(\gamma\) is the path loss exponent reflecting the environment, and \(X_{g}\) is a random variable accounting for channel variations such as fading. Using the model, we define the following two functions. (We set \(X_{g}\) to 0, and use the margin parameter to account for channel variations). \[D2 PL(d)=PL_{0}+10\gamma\log_{10}\frac{d}{d_{0}} \tag{5}\]  
Figure 2: An example network scenario for calculating CST. Distance between the transmitting node and the interfering node is estimated based on a pathloss model, and CST is calculated based on the distance. \[PL2D(P)=d_{0}\times 10^{\frac{P-PL_{0}}{10P}} \tag{6}\]  
_D2 PL_ converts distance to path loss, whereas _PL2D_ estimates distance from path loss. Suppose the distance between AP1 and node S is \(d_{1}\), and the distance between AP2 and node S is \(d_{2}\). Using the _PL2D_ function, we calculate estimated values of \(d_{1}\) and \(d_{2}\). \[d_{1}=PL2D(PL_{1})=PL2D(P_{TX}-P_{1}) \tag{7}\]  
\[d_{2}=PL2D(PL_{2})=PL2D(P_{TX}-P_{2}) \tag{8}\]  
In the equations, \(P_{TX}\) is the transmit power, which we assume is fixed and the same for every node. \(PL_{1}\) and \(PL_{2}\) are the path loss between AP1 and S, and AP2 and S, respectively. Since AP2 is at the opposite position of AP1 from node S, the distance between AP1 and AP2 is \(d_{1}+d_{2}\). Thus, we can calculate the received signal strength of AP1 at AP2 (\(P^{\prime}\)) using the _D2 PL_ function as follows.