## 6 Simulation Results  
This section presents performance comparison between SU and MU-network MIMO with the power management methods. Unless otherwise stated, the cell radius \(R\) and cell-center radius \(D\) are 1000 m and 787.55 m, respectively. Accordingly, within a sector, the ratio of cell-center area to cell-edge area is 3 to 1. Assume users are uniformly distributed in each cell. Thus, we set the ratio of sub-channel number between inner band \(f_{A}\) and outer band \(f_{B}\) to be 3 to 1 as well. To this end, we assume the total number of OFDMA sub-channels is 60 such that the numbers of sub-channels in \(f_{A}\) and \(f_{B}\) are integers 45 and 15, respectively. Therefore, each outer sub-band \(f_{Bi}\) consists of 5 OFDMA sub-channels. As a result, for SU-network MIMO, there are at most five active CEUs in each sector (hard CEU capacity). As for MU-network MIMO, joint preprocessing makes it possible that more than five CEUs in each sector can be served at the same time (soft CEU capacity). Assume there are 12 subcarriers in a sub-channel and the sub-channel bandwidth \(W\) is 138.8 KHz. The maximum power constraint \(P_{\text{max}}\) is 46.523 dBm [2]. The propagation constant \(\beta_{0}\) and path loss exponent \(\gamma\) are \(1.35\times 10^{7}\) and 3, respectively [20]. The standard deviation of log-normal shadowing is 12 dB. Unless otherwise stated, there are 15 CCUs (\(x=15\)) and 5 CEUs (\(y=5\)) uniformly distributed in each sector, each sector is equipped with five transmission antennas \((N_{\text{T}}=5)\) and the power coefficient is one (\(\alpha=1\)). As for users, each of them is equipped with a single receiver antenna \((N_{\text{R}}=1)\). In terms of different values of \(K_{\text{max}}\), Figure 2 shows the capacity comparison for SU-network MIMO and Figure 3 presents its corresponding curves of power reduction factors. In Figure 2, we find that smaller \(K_{\text{max}}\) yields better per-user (average) capacity than larger \(K_{\text{max}}\). However, smaller \(K_{\text{max}}\) results in bigger capacity gap between CCU and CEU than larger \(K_{\text{max}}\). Thus, through continuing enlarging the value of \(K_{\text{max}}\), the capacity gap can be reduced, but it is at the cost of decreasing the average capacity. For example, in Figure 2, an equal CCU and CEU capacity (zero capacity gap) occurs at about \(K_{\text{max}}=0.513\), i.e., a uniform capacity is achieved regardless of user position; however, it obviously reduces the average capacity. Figure 3 shows that while the value of \(K_{\text{max}}\) is increasing, the power factor \(\rho_{1}\) is increasing as well. This is because a larger value the \(K_{\text{max}}\) means that more transmitter power is allocated to the inter-cell CEUs. Accordingly, the power factor \(\rho_{2}\) associated with intra-cell users is decreasing while the value of \(K_{\text{max}}\) is increasing. Figure 2: Capacity comparison for SU-network MIMO in terms of different values of \(K_{\text{max}}\). As a function of power coefficient \(\alpha\), Figure 4 shows the capacity comparison for SU-network MIMO with a small \(K_{\max}\) (say \(K_{\max}=0.25\)). Please note that the CEU power is given by \(P_{E}=P_{E}^{\prime}=\alpha P_{\rm C}\). Thus, we can raise the CEU power by increasing the value of \(\alpha\). It is found that increasing the value of \(\alpha\) can actually diminish the capacity gap between CCU and CEU, and a uniform capacity is achieved at \(\alpha=275\). However, the average (per-user) capacity is also slowly decreasing at the same time, while the capacity gap is decreasing. In Figure 5, we present the capacity comparison as a function of \(\alpha\) for a large \(K_{\max}\) (say \(K_{\max}=0.4\)).