# Improving Spatial Reuse of Wireless LAN Uplink Using BSS Color and Proximity Information
## 3 Proposed Method
### Protocol Details
#### 3.2.3 Protocol Operation
Once we get \(d_{12}\) and \(d_{1A}\), we estimate \(d_{2A}\) as Equation (14), which is the worst case in terms of interference at AP\({}_{2}\). \[d_{2A}=d_{12}-d_{1A} \tag{14}\]  
Once we get \(d_{2A}\), we convert it back to pathloss \(P_{2A}\) using Equation (12). Then, by subtracting the pathloss from transmit power, we get \(P_{2A}\). Finally, we can use Equation (11) to determine whether the packet transmitted from node B will be successfully received at AP\({}_{2}\). If Equation (11) is true, then AP\({}_{2}\) can successfully receive the packet from node B. If Equation (11) is false, then AP\({}_{2}\) will not have sufficient SNR to receive the packet from node B. In the second case, we estimate \(d_{2A}\) using the distance between two senders (\(d_{AB}\)) and the distance between node B and AP\({}_{2}\) (\(d_{2B}\)). In this case, the worst case would be when AP\({}_{2}\) is located on the line connecting node A and node B. Then, the distance between node A and AP\({}_{2}\) is \(d_{AB}-d_{2B}\). Similar to the previous case, we convert \(P_{AB}\) and \(P_{2B}\) to \(d_{AB}\) and \(d_{2B}\). \(P_{AB}\) can be obtained by measuring signal strength of the packet from node A, and \(P_{2B}\) can be obtained from B's neighbor table. We convert these values to distances using the pathloss model, estimate the worst-case distance \(d_{2A}\) using Equation (15), and convert the value back to pathloss to get \(P_{2A}\). In this case as well, we can use Equation (11) to determine whether AP\({}_{2}\) can successfully receive the packet from node B.  
\[d_{2A}=d_{AB}-d_{2B} \tag{15}\]  
In summary, when node B receives preamble from node A, node B calculates \(d_{2A}\) according to Equations (14) and (15). Then, according to Equation (8), we choose the final \(d_{2A}\) as the maximum of the two. Then, we convert \(d_{2A}\) into the \(P_{2A}\) and apply Equation (11) to determine whether the packet transmitted by node B will be successfully received at AP\({}_{2}\). If Equation (11) is true, the node B can continue its backoff countdown and transmit concurrently with the ongoing communication. If Equation (11) is false, node B must pause its backoff and defer its transmission. The whole process of the proposed scheme is described as a flow diagram in Figure 6.  
In the beginning of the section, we assumed that the nodes transmit packets at the same transmit power. However, it is possible that a user station could reduce the transmit power in order to reduce interference or other reasons such as energy conservation. In this case, the transmit power must be taken into account when calculating the interference at the receivers. In the proposed scheme, the only term affected by the transmit power of the user station is \(d_{AB}\), which is the distance between the two user stations. All the other distances are calculated from RSSIs measured from beacons that are transmitted using a fixed transmit power. In order to correctly estimate \(d_{AB}\), node B needs to know the transmit power of node A. There are two ways to address this problem. First, node A encodes its transmit power into the preamble, similar to the proximity information. This will require several bits in the preamble, which is an overhead. An alternative is to just assume that node A is transmitting at the maximum transmit power. Then, the calculation of \(d_{AB}\) will result in a larger value when node A is transmitting at a reduced power. In turn, \(d_{2A}\) will be estimated as a larger value, and \(P_{2A}\) will be estimated as a smaller value. As node A is transmitting at a reduced power, \(P_{2A}\) will actually be smaller than when node A is transmitting at the maximum power. Although estimation errors will increase because pathloss is a nonlinear function, we do not need to explicitly send transmit power in the preamble in this scheme. When calculating SNR in Equations (10) and (11), we use the margin parameter \(m\) to account for channel variation due to fading, as well as errors made from the pathloss model.