# On the Virtual Cell Transmission in Ultra Dense Networks
## 1 Introduction
### Our Contribution  
In this paper, we focus on the user-centric scheme, where only partial coordination is required and can scale well with the network size. Different from the virtual cell grouping scheme proposed in [11], where users whose virtual cells overlap with each other are grouped into a new virtual cell, this paper groups the virtual cells that overlap in the interference domain. Specifically, we first construct an interference graph that stands for the potential interference relationship among the virtual cells, whereby virtual cells having a potential ICI stronger than a predefined threshold are connected. Then, RBAs and users in the virtual cells within the same maximally-connected component (MCC) are grouped together and merged into one new virtual cell cluster. The grouped users are jointly served by the merged virtual cell via zero-forcing (ZF) to eliminate the intra-cluster interference. During the ZF transmission, coordination takes place only within the merged virtual cell, and no inter-cell information exchange is required. Due to the remaining inter-cluster interference after cell merging, we propose to use multi-virtual-cell minimum mean square error (MVC-MMSE) precoding where only the exchange of cross cell CSI is required. Considering that the achievable rate is influenced mainly by the strong interference and is quite insensitive to the weak interference, we propose to use IA to simultaneously align the strongest interference on a lower dimensional subspace at each receiver, so that the desired signals can be transmitted on the interference-free dimensions. Simulation results validate the effectiveness and performance gain of the proposed transmission schemes in the UDN.  
The contributions of this paper can be summarized in the following aspects:  
* This paper proposes a user-centric scheme, where only partial coordination is required, and can scale well with the network size.
* This paper proposes an interference graph-based virtual cell merging scheme, where the size of the merged virtual cells can be well scaled by tuning the interference graph threshold. Then,the grouped users are jointly served by the merged virtual cell via ZF and MVC-MMSE to eliminate the intra-cluster and inter-cluster interference.
* This paper proposes IA within every cluster based on the virtual cell merging scheme, which aims to eliminate strong intra-cluster interference.  
The remainder of the paper is organized as follows. In Section 2, the system model is introduced. Section 3 describes details about the virtual cell merging scheme based on the interference graph and applies different precoding schemes, such as ZF, MVC-MMSE and IA, to the merged virtual cell clusters. Simulation results of average user spectral efficiency are presented with different transmission schemes in Section 4, and Section 5 concludes this paper.  
Notation: We use lowercase and uppercase boldface letters for column vectors and matrices, respectively; \((\cdot)^{T}\), \((\cdot)^{H}\) and \((\cdot)^{-1}\) for the transpose, conjugate transpose and inversion of a matrix, respectively. \(A_{i,j}\) denotes the entry in the \(i\)-th row and \(j\)-th column of matrix \(\mathbf{A}\). The \(N\times N\) identity matrix is denoted by \(\mathbf{I}_{N}\). \(\mathbb{E}(\cdot)\) denotes the expectation of a random variable. \(\odot\) denotes the Hadamard product. eigvec\((\cdot)\) denotes the eigenvector of the matrix. \(\left\|\cdot\right\|\) denotes the norm of the matrix.