# A Throughput Analysis Using a Non-Saturated Markov Chain Model for LTE-LAA and WLAN Coexistence
## 3 Performance Evaluation  
We obtained numerical results for the throughput of each system in a coexistence scenario involving LTE-LAA and WLAN systems. As illustrated in Figure 1, we assumed a scenario for performance evaluation where a single LTE-LAA small cell coexists with multiple WLAN access points (APs) operating at a carrier frequency of 5.8 GHz over a 20 MHz bandwidth. Within the LTE-LAA cell, 10 LTE-LAA devices were uniformly distributed, and within a cell of radius \(R_{I}\), five or fifteen APs were also uniformly located. Each AP was connected to five WLAN nodes. The urban micro non-line-of-sight model for a hexagonal cell layout was used to estimate the path loss [12]. Here, with \(r\) representing the distance in meters and \(f_{c}\) the carrier frequency in GHz, the path loss was given by \(PL=36.7\log_{10}\left(r\right)+22.7+26\log_{10}\left(f_{c}\right)\) (dB). This yields the corresponding values of \(K=10^{-7.254}\) and \(\eta=3.67\)[18]. The other parameters required for our performance evaluation were as follows: \(P_{a}=20\) dBm, \(P_{s}=17\) dBm, \(P_{e}=30\) dBm, \(P_{N}=-90\) dBm, \(W_{0}=16\), \(R_{I}=40\) m, \(\kappa_{bw}=0.6726\), \(\kappa_{c}=0.75\), \(\kappa_{sint}=1\), \(B=20\) MHz, \(DIFS=34\)\(\mu\)s, \(SIFS=16\)\(\mu\)s, \(\sigma=9\)\(\mu\)s.  
The WLAN transmission rate, \(R_{W}\), was set to 72 Mbps, while the rate for LTE-LAA can be calculated using Equation (21). The medium access control and physical layer header sizes were set to 272 bits and 128 bits, respectively. The acknowledgment packet was configured with 336 bits, and the payload size was 12,000 bits. The durations \(T_{u,s}\), \(T_{u,c}\), \(T_{w,s}\) and \(T_{w,c}\) were influenced by \(R_{W}\), \(R_{U}\), the sizes of headers, acknowledgments, and payload, as well as DIFS, SIFS, and the propagation delay [21]. The propagation delay was set to 2 \(\mu\)s.  
To examine how the contention window size \(W\) at the LTE-LAA eNB affects throughput, Figures 7 and 8 present the average throughput versus \(W\) for LTE-LAA, WLAN, and the total system (i.e., LTE-LAA+WLAN). It can be observed that, as \(W\) increases, the average WLAN throughput increases while the throughput of the LTE-LAA system decreases. This is due to the LTE-LAA eNB experiencing longer backoff durations as \(W\) increases, allowing WLAN nodes more frequent access to the channel. Moreover, Figures 7 and 8 illustrate that the average throughput of the LTE-LAA system is lower when fifteen APs are positioned within a cell radius \(R_{I}\), compared to when only five APs are positioned. This is due to the fact that having fifteen APs increases the number of WLAN basic service sets within the CCA range compared to having only five APs.  
Figures 9 and 10 demonstrate that the average throughput of both LTE-LAA and WLAN systems is highly influenced by the CCA threshold, \(P_{cca}\), at the LTE-LAA eNB. These figures also reveal distinct operational behaviors between the two systems. For WLAN, the average throughput continuously decreases as \(P_{cca}\) increases. In contrast, the LTE-LAA throughput, shown in Figure 10, increases as \(P_{cca}\) approaches \(-79\) dBm and then gradually declines as \(P_{cca}\) continues to increase. Note that a higher CCA threshold reduces the number of WLAN basic service sets within the CCA range, while the interference experienced by the LTE-LAA device, caused by concurrent transmissions of WLAN nodes in the interfering area, intensifies with an increase in \(P_{cca}\).  
Figure 8: Average throughputs of LTE-LAA and WLAN systems versus \(W\) when 15 APs are positioned within a cell radius \(R_{I}\).  
Figure 10: Average throughputs of LTE-LAA and WLAN systems versus \(P_{cca}\) when 15 APs are positioned within a cell radius \(R_{I}\).  
Figure 9: Average throughputs of LTE-LAA and WLAN systems versus \(P_{cca}\) when 5 APs are positioned within a cell radius \(R_{I}\).