## 5 Performance Evaluation
### Impact of ICI by Comparing TCG and CGI  
In this subsection, we randomly deploy five picocells with identical radii in each round of simulation. For different curves in each figure, the radii of picocells vary from 100-300 m. In order to achieve different coverage radii for picocells, we set the transmission power for devices selecting picocells as \(-9\), \(-3\) and 0.5 dBm for picocell radii equaling 100, 200 and 300 m when the path loss exponent is two (free space). When the path loss exponent is three (suburbs), the transmission power is set to \(-9\), 0 and 5.3 dBm, respectively. Additionally, when the path loss exponent is four (downtown), they are set to \(-9\), 3 and 10 dBm. Because the magnitude of ICI changes along with the change of the path loss exponent, the collapse point for the weight of ICI varies for different path loss exponents. We compare TCG and CGI to show the collapse in Figure 6. The x-axis is the weight of ICI, so that we could easily see the collapse of the PSNE of the CGI model and the degradation of the system performance with regard to the severity of the ICI. Note that curves for TCG in Figure 6 correspond to the PSNE, while curves for CGI do not correspond to the PSNE, but the average feature of the CGI model. As explained for Figures 4a and 5b, once a device collapses to the macrocell, the PSNE collapses to all zeros without any equilibrium between \(N_{i}\) and zero. Therefore, curves for CGI in Figure 6a, c and e actually show the average of \(n_{i},i=1,...,5\) for a number of rounds of simulations. Since the devices' deployment and the BSs' locations vary round by round, the collapse points vary, as well. Actually, in each round, the collapse points for different picocells may not be the same either due to the difference of their locations. The average value of \(n_{i}\) for a given cell radius and the weight of ICI can be considered as an average measure of CS preference between picocells and the macrocell. Seen from each subfigure above, the PSNE has larger probability to collapse when the weight of ICI becomes larger, indicating the impact of ICI on the PSNE. Comparing the three subfigures, when the path loss exponent is small, PSNE collapse in a relatively small weight of ICI, indicating the severity of ICI with regard to the path loss exponent. In Figure 6b, d and f, spatial spectral efficiency with Path Losses 2, 3 and 4 are shown, respectively. The spatial spectral efficiency at each point in each curve is calculated as the summation of all of the devices' total capacity divided by the system bandwidth and the macrocell disc area (in km\({}^{2}\)). We can see that the average spatial spectral efficiency decreases after the PSNE collapses. Note that, TCG does not consider the ICI at all, so its PSNE and corresponding average spatial spectral efficiency do not change along with the weight of ICI, as shown in all of the above subfigures. As we know, for the macrocell, its advantage is the low ICI, while the disadvantage is the small available bandwidth due to the large number of connected devices. By contrast, for the picocells, the advantage is the large available bandwidth, while the disadvantage is severe ICI from the macrocell. Therefore, it is not difficult to understand the simulation results in Figure 6. Devices approaching  
Figure 6: Impact of ICI on CS preference and spatial spectral efficiency using TCG and the congestion game with ICI (CGI). (**a**) Path Loss 2 (free space); (**b**) Path Loss 2 (free space); (**c**) Path Loss 3 (suburbs); (**d**) Path Loss 3 (suburbs); (**e**) Path Loss 4 (downtown); (**f**) Path Loss 4 (downtown). picocell BSs obtain larger spectral efficiency by using picocells because of the larger amount of obtained bandwidth and better channel condition to these BSs. When the radii of the picocells are large, more devices will change their preferences during the collapse, so the decrement of spatial spectral efficiency will be large, which is clearly shown in all of the above subfigures.