## 5 Performance Evaluation
### Impact of ICI by Comparing CGC-FFR and CGC-OFD  
The configuration for this subsection is similar to Section 5.2, except for the bandwidth and the transmission power are configured as follows. For CGC-FFR, the whole system bandwidth is used in the same way as before. By contrast, for CGC-OFD, the whole bandwidth is divided into two portions, _i.e._, 2/3 for the macrocell and 1/3 for each picocell. The transmission powers for the picocells with 100 m radii are variable for the x-axis, from \(-\)80-20 dBm, while the transmission powers for the picocells with 200 m and 300 m radii are calculated with an augmentation as before to guarantee the increment of the picocell radii, _i.e._, 6 and 9.5 dBm augmentation for a path loss exponent equaling two; 9 and 14.3 dBm augmentation for a path loss exponent equaling three; and 12 and 19 dBm augmentation for a path loss exponent equaling four. Note that the transmission power of a device selecting a picocell should not be as low as \(-\)80 dBm, but we keep the x-axis range large to show the collapse clearly and to compare between CGC-FFR and CGC-OFD.  
Figure 7a,c,e shows the collapse of the PSNE for a path loss exponent equaling 2, 3 and 4, respectively. We can see that, when the transmission power of picocells decreases, both of the two games' PSNE collapse. The difference is that CGC-OFD keeps a number of devices selecting picocells in the normal transmission power range, while the ICI in CGC-FFR already makes the PSNE collapse to the macrocell. Besides, by increasing the path loss exponent, the gap between the curves of CGC-FFR and CGC-OFD becomes smaller. That is because the large path loss exponent decreases ICI, hence reducing the difference of the two games. Based on the analysis in Figure 4b and our experience with extensive simulations, the collapse feature of CGC is different from that of CGI. Instead of suddenly collapsing to all zeroes, the PSNE of CGC decreases gradually from \(N_{i}\) to zero, little by little.  
The system's average spatial spectral efficiencies with a path loss exponent equaling 2, 3 and 4 are shown in Figure 7b,d,f, respectively. Different from the previous subfigures showing a saturated point where a curve becomes flat, curves in these three subfigures will keep on increasing along with the increase of the transmission power of picocells. We can see that, first, the curves of CGC-FFR are higher than those of CGC-OFD, indicating that, suffering severe ICI, it is still suggested to reuse the frequency. Second, when the path loss exponent is large, the difference of the spatial spectral efficiencies of the two games decreases due to the decrease of ICI. Third, the curves with larger picocells have better system performance, indicating that, seen from the system's point of view, it is still important to keep a number of devices on the side of picocells, _i.e._, the PSNE collapsing to the macrocell is generally an undesired result.  
Figure 7: Impact of ICI on CS preference and spatial spectral efficiency using CGC-fractional frequency reuse (FFR) and CGC-orthogonal frequency division (OFD). (**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).