# On the Virtual Cell Transmission in Ultra Dense Networks
## 5 Conclusions  
This paper aims to mitigate the large and complex interference in downlink UDN. Different from the traditional BS-centric cellular approach and the complex and time-consuming global optimal solution, a user-centric virtual cell paradigm is adopted. An interference graph-based virtual cell merging scheme is proposed in comparison with the overlapping-based virtual cell merging approach. After the interference graph is created, RBAs and users in the virtual cells within the same maximal connected component are grouped together and merged into one new virtual cell cluster, where users are jointly served via ZF. MVC-MMSE-based transmission schemes are further proposed to enhance the performance of the two virtual cell merging methods, which is shown to be effective for VCMO. Additionally, the interference alignment algorithm is proposed based on the improved virtual cell merging to eliminate the strong interference between different virtual cells. Simulation results show that the proposed ZF-VCMG and MVC-MMSE-VCMO can attain the average user spectral efficiency performance of ZF-VCMO with a much smaller virtual cell cluster size and significantly reduced signal processing complexity. Besides, the proposed user-centric transmission schemes greatly outperform the BS-centric transmission scheme (MRT) in terms of both the average user spectral efficiency and edge user spectral efficiency. What is more, IA based on the low complexity virtual cell merging can achieve much better performance than ZF and MRT precoding in terms of average user spectral efficiency. With the increased number of \(P/\sigma^{2}\) and \(\rho\), IA leads to more improvement and low complexity in average user spectral efficiency gain, compared to ZF and MRT. This indicates that the proposed scheme scales much better with the network density than ZF and MRT without merging, revealing that it can be applied suitably in ultra dense networks. Additionally, this paper treats all of the users equally without differentiating them based on the channels. Therefore, the precoding performance could be further improved by applying appropriate power control or IA algorithms.  
This work was supported by China's 863 Project (No. 2015 AA01A706), the National Science and Technology Major Project (No. 2016 ZX03001017), Science and Technology Program of Beijing (D161100001016002), the Scientific and Technological Cooperation Projects (No. 2015 DFT10160B) and by the State Key Laboratory of Wireless Mobile Communications, Samsung, and China Academy of Telecommunications Technology (CATT).  
**Author Contributions:** The work presented in this paper corresponds to a collaborative development by all authors. [PERSON] and [PERSON] defined the research line. [PERSON] and [PERSON] developed the proposed algorithm and wrote the paper. [PERSON] gave many modification suggestions about the paper. All authors have read and approved the final manuscript.  
**Conflicts of Interest:** The authors declare no conflict of interest.  
Figure 9: Average user spectral efficiency versus \(P/\sigma^{2}\) for different interference management algorithms, with \(K=51\), \(\rho=10\), \(\rho=20\) and \(D=N_{0}=2\).