# On the Virtual Cell Transmission in Ultra Dense Networks
## 3 Transmission Schemes Based on Virtual Cell Merging
### Virtual Cell Merging with ZF and MVC-MMSE Transmission
Figure 4: Average user spectral efficiency of maximum ratio transmission (MRT), ZF-virtual cell overlapping (VCMO) and MVC-MMSE-VCMO versus initial virtual cell size \(N_{0}\), with \(K=50\), \(\rho=20\) and \(\rho=200\). Since both VCMO and VCMG can significantly improve \(\overline{R}\), both at the price of the increase of signal processing complexity or signaling overhead, Figures 6 and 7 show the average cluster size and maximal cluster size of these transmission schemes respectively, when different \(\overline{R}\) are reached. It should be noted that with the given \(\rho\), the signaling overhead required for MVC-MMSE scales linearly with the average cluster size, while the signal processing complexity required for ZF or MVC-MMSE scales linearly with the cube of the maximal cluster size. It can be clearly seen that the ZF-VCMG scales much better than ZF-VCMO in terms of both average and maximal cluster size. ZF-VCMG can attain almost the same maximal cluster size as MVC-MMSE-VCMO when the targeted \(\overline{R}\) is low and can further achieve higher \(\overline{R}\) at a much smaller maximal cluster size than ZF-VCMO and MVC-MMSE-VCMO. This indicates that ZF-VCMO can achieve a targeted \(\overline{R}\) with much lower signal processing complexity while no inter-cluster CSI exchange is needed. One may argue that the curves for ZF-VCMG and MVC-MMSE-VCMG become more and more steep with the increase of the maximal cluster size in Figure 7. This brings a very sharp increase of average user spectral efficiency when the maximal cluster size is around 100. In fact, the maximal cluster size is upper bounded by \(K\times N_{0}\), which corresponds to the situation that all users' initial virtual cells merge into one cluster. With the increase of \(\varphi\), the average cluster size grows; so does the maximal cluster size, but it cannot exceed \(K\times N_{0}\), which is the upper bound. When the maximal cluster size is close to the upper bound, a marginal further increase of the maximal cluster size may bring remarkable growth in the average cluster size, so we can still see a significant increase of the average user spectral efficiency. This leads to a large slope of the corresponding curves around the upper bound. However, the average user spectral efficiency will not increase infinitely due to the limited number of transmitting antennas. As a result, the average and maximal cluster size of ZF-VCMG and MVC-MMSE-VCMG can be well controlled by \(N_{0}\) and \(\varphi\), while that of ZF-VCMO and MVC-MMSE-VCMO is totally out of control, especially when the network is ultra dense. Figure 5: Average user spectral efficiency of MRT, ZF-virtual cell merging based on the interference graph (VCMG) and MVC-MMSE-VCMG versus relative interference graph threshold \(\varphi\), with \(K=50\), \(\rho=20\) and \(\rho=200\). Figure 8 presents the cumulative distribution function (CDF) of \(\overline{R}\) for different transmission schemes. It can be clearly seen that \(\overline{R}\) of the VCMO- and VCMG-based transmission schemes are distributed in a much smaller range than MRT, indicating that the user-centric virtual cell can effectively eliminate the cell edge in the UDN, thus greatly reducing the performance difference among the users. As a result, the user spectral efficiency performance is much less sensitive to the users' positions than the BS-centric scheme is, stepping towards the goal of consistent high quality of experience (QoE) in UDN. We can also observe that ZF-VCMG outperforms MRT and ZF-VCMO significantly in terms of both average user spectral efficiency and edge user spectral efficiency. MVC-MMSE-VCMO can attain the performance of ZF-VCMG if \(B\) is large enough, but inter-cluster CSI exchange is required. MVC-MMSE-VCMG almost makes no contribution to the right shift of the CDF curves, although additional inter-cluster CSI exchange is provided. Figure 6: Average user spectral efficiency of ZF-VCMO, MVC-MMSE-VCMO, ZF-VCMG and MVC-MMSE-VCMG versus the average cluster size, with \(K=50\), \(\rho=20\) and \(\rho=200\).