text: This paper proposes a linear interference alignment (IA) scheme which can be used for uplink channels in a general multicell multiuser MIMO cellular network. The proposed scheme aims to align interference caused by signals from a set of transmitters into a subspace which is established by the signals from only a subset of those transmitters, thereby effectively reducing the number of interfering transmitters. The total degrees of freedom (DoF) achievable by the proposed scheme is given in closed-form expression, and a numerical analysis shows that the proposed scheme can achieve the optimal DoF in certain scenarios and provides a higher total DoF than other related schemes in most cases.
  @cite_24: This paper investigates the symmetric degrees of freedom (DoF) of MIMO cellular networks with G cells and K users per cell, having N antennas at each base station and M antennas at each user. In particular, we investigate achievability techniques based on either decomposition with asymptotic interference alignment (IA) or linear beamforming schemes, and show that there are distinct regimes of (G,K,M,N) where one outperforms the other. We first note that both one-sided and two-sided decomposition with asymptotic IA achieve the same degrees of freedom. We then establish specific antenna configurations under which the DoF achieved using decomposition based schemes is optimal by deriving a set of outer bounds on the symmetric DoF. For linear beamforming schemes, we first focus on small networks and propose a structured approach to linear beamforming based on a notion called packing ratios. Packing ratio describes the interference footprint or shadow cast by a set of transmit beamformers and enables us to identify the underlying structures for aligning interference. Such a structured beamforming design can be shown to achieve the optimal spatially normalized DoF (sDoF) of two-cell two-user cell network and the two-cell three-user cell network. For larger networks, we develop an unstructured approach to linear interference alignment, where transmit beamformers are designed to satisfy conditions for IA without explicitly identifying the underlying structures for IA. The main numerical insight of this paper is that such an approach appears to be capable of achieving the optimal sDoF for MIMO cellular networks in regimes where linear beamforming dominates asymptotic decomposition, and a significant portion of sDoF elsewhere. Remarkably, polynomial identity test appears to play a key role in identifying the boundary of the achievable sDoF region in the former case.
  @cite_19: 
  @cite_2: We propose an interference alignment scheme for the L cell multiuser interference channel, where M antennas are used at the base stations and N antennas are used at user terminals. To handle the large number of interference vectors from other cells, the proposed method aligns interference vectors such that they fall in a rank one vector space at the other cell base station receivers. After the alignment, we can achieve the sum DoF (K) values of, K=M when N <; 2(L-1), K=L(M-1) when N≥ (L-1)M. For other cases, we can achieve K=M-L+(L-1) [N L-1] in the L cell interference network, where [·] is the integer floor function.
  @cite_16: For a three-cell constant cellular interfering network, a new property of alignment is identified, i.e., an interference alignment (IA) solution obtained in a user-cooperation scenario can also be applied to a non-cooperation environment. By using this property, an algorithm is proposed by jointly designing transmit and receive beamforming matrices. Analysis and simulation results show that more degrees of freedom (DoF) can be achieved compared with conventional schemes in most cases.
  @cite_10: In this letter, the degrees of freedom (DoF) outer bound is characterized for an L-cell constant cellular interfering network by using linear interference alignment (IA). For a symmetric network, it means that no matter how many cells and users per cell there are, the total achievable DoF is bounded by M+N, where M and N denote the number of antennas equipped on users and base stations. Besides, a DoF achievable algorithm is also proposed. Although the DoF outer bound cannot be reached, more DoF can be obtained compared with orthogonal schemes.
summary: For general multicell multiuser uplink channels, @cite_24 proposed a new scheme called unstructured IA scheme which appeared to provide a high DoF performance, but for a given uplink channel the feasibility of the scheme cannot be determined until the scheme is actually applied and checked by a numerical test. On the other hand, the IA scheme in @cite_2 aimed to align ICI into a one-dimensional subspace, and because this IA constraint was too stringent to be satisfied, only a fraction of the ICI could be aligned. This problem was then resolved in @cite_19 by consolidating ICI into a multi-dimensional subspace rather than a one-dimensional subspace. By extending the scheme in @cite_16 , which was designed only for three-cell multiuser uplink channels, the scheme in @cite_10 can be applied to a general uplink channel; however, its DoF performance decreases when the size of the uplink channel increases as the scheme can only suppress the interference caused by one interfering user regardless of the size of the uplink channel.