# A Channel Measurement-Based Listen-Before-Talk Algorithm for LTE-LAA and WLAN Coexistence
## 3 Proposed CM-LBT Scheme
### Throughput Estimation of LTE-LAA and WLAN Systems  
We estimate the throughput of LTE-LAA and WLAN systems by considering both their channel access activities and CCA at LTE-LAA eNB, as presented in Sections 3.1 and 3.2. To this end, the CM-LBT scheme must additionally know the channel usage of the WLAN nodes, which can be obtained through the channel measurement. That is, the LTE-LAA eNB measures the transmission and collision probabilities of WLAN nodes, as well as the probability that the medium is sensed as idle, when the CCA threshold is set to \(P_{cca}\). We assume that LTE-LAA eNB can distinguish the individual WLAN signals with higher accuracy by being equipped with a signal detector [7]. LTE-LAA eNB periodically records the transmission state (idle or transmitting) of WLAN nodes at each slot. We denote \(N_{tot}\) and \(N_{tx}\) as the total number of slots to which the LTE-LAA eNB is not transmitting and to which one or more WLAN nodes are transmitting, respectively, when the CCA threshold of LTE-LAA eNB is \(P_{cca}\). We can then obtain the probability that one or more WLAN nodes within the CCA range are attempting transmission in a typical slot as follows [5; 19]:  
\[\tau_{w}(P_{cca})=N_{tx}/N_{tot}. \tag{17}\]  
Then, the collision probability given LTE-LAA eNB attempting transmission is \(p=\tau_{w}(P_{cca})\). The probability that the medium will be sensed as idle is simply the probability that the next slot is empty given that LTE-LAA eNB is not transmitting. i.e., \(P_{idle}=1-\tau_{w}(P_{cca})=1-p\). We assume that LTE-LAA eNB can detect a collision among the transmissions of WLAN nodes by means of power sensing and signaling processing in the time domain [5; 21]. Let \(N_{c}\) denote the number of slots in which a collision occurs of the transmissions of WLAN nodes when the CCA threshold is \(P_{cca}\). Then, the collision probability is \(p_{w}(P_{cca})=N_{c}/N_{tx}\). The length of the channel usage state is not a fixed period of real-time. The channel usage state may be occupied by a successful transmission of LTE-LAA eNB or a WLAN node, a collision of the transmissions of LTE-LAA eNB and WLAN nodes, or a collision of only WLAN nodes. Otherwise, the medium may be idle. Using Equation (10), the probability that at least LTE-LAA eNB or one of the WLAN nodes will attempt transmission is as follows:  
\[P_{tr}=1-\{1-\tau_{w}(P_{cca})\}\{1-\tau(W)\}. \tag{18}\]  
The probabilities that LTE-LAA eNB and one of the WLAN nodes, respectively, will successfully transmit are as follows:  
\[ \begin{split} P_{u,s}=\tau(W)\{1-\tau_{w}(P_{cca})\},\\ P_{w,s}=\tau_{w}(P_{cca})\{1-p_{w}(P_{cca})\}\{1-\tau(W)\}.\end{split}  \tag{19}\]The probabilities that LTE-LAA eNB and only WLAN nodes, respectively, experience a collision by attempting transmission are given by the following:  
\[ \begin{split} P_{u,c}=\tau_{w}(P_{cca})\cdot\tau(W),\\ P_{w,c}=\tau_{w}(P_{cca})\cdot p_{w}(P_{cca})\{1-\tau(W)\}.\end{split}  \tag{20}\]  
LTE-LAA eNB measures the expected times taken for a successful transmission from itself and the WLAN nodes denoted by \(T_{u,s}\) and \(T_{w,s}\), respectively. Additionally, the expected times taken for a collision that LTE-LAA eNB and the WLAN node experience are denoted by \(T_{u,c}\) and \(T_{w,c}\), respectively. Then, when the CCA threshold is \(P_{cca}\), the expected time spent per state is as follows:  
\[E_{s}(P_{ccca})=(1-P_{tr})\sigma+P_{u,s}T_{u,s}+P_{w,s}T_{w,s}+P_{u,c}\cdot max \{T_{u,c},T_{w,c}\}+P_{w,c}T_{w,c}. \tag{21}\]  
where \(\sigma\) is the slot time. Using Equation (21), we can estimate \(q\), the probability that a packet will become available to the medium access control of LTE-LAA eNB in an expected slot time. LTE-LAA eNB first measures the mean inter-packet time, \(t_{p}\). We assume packets arrive at the medium access control in a Poisson manner with rate \(\lambda_{p}^{(u)}=1/t_{p}\).