On Feasibility of Interference Alignment for L-Cell Constant Cellular Interfering Networks

On the Achievable Degrees of Freedom of Two-Cell Multiuser MIMO Interference Networks

“…We explicitly formulate the necessary and sufficient grouping rules for obtaining a feasible solution to the rank minimization problem (Theorem 1). The derived achievable sum DoF based on the GA is greater than existing results [16], [17] and achieves the upper bounds derived in [3], [8], [14], [22] in some cases. 2) We derive the achievable sum DoF for a particular case of interest.…”

“…For 1), it is in general difficult to establish a coding structure that produces non-trivial precoding vectors for the data streams in a group with an arbitrary packing ratio, as the problem is related to algebraic geometry and is open in general [8], [22]. Thus, we consider a restricted form of the problem by focusing on two types of packing ratios, namely, κ g : 1 (where κ g ∈ N + ) and κ g : κ g − 1 (where κ g ∈ N + and κ g ≥ 3), for which we can show that they lead to a feasible solution to Problem P. Note that any arbitrary packing ratio can be treated as a combination of one or both of these two types of packing ratios (e.g., the packing ratio 5 : 3 can be decomposed into 3 : 1, 1 : 1, 1 : 1; or 2 : 1, 3 : 2; or 2 : 1, 2 : 1, 1 : 1), although the resulting coding structures will lead to suboptimal solutions compared to what would be yielded with a general coding structure.…”

“…For 2), we establish three grouping rules in the following based on the coding structure in (22) to find a proper composition of data streams in each group. The three grouping rules will be shown to be necessary and sufficient conditions for the GA to produce a feasible solution to Problem P. Then, we present the general procedure of the GA based on the three grouping rules.…”

“…A smaller dimension of the interference subspace therefore leads to a greater dimension of the signal subspace. Interference alignment (IA), first introduced by Maddah-Ali et al [1] as well as Cadambe and Jafar [2], is based on the idea of aligning multiple interfering signals into a subspace of provably smallest dimension such that the dimension of the signal subspace is increased as much as possible for the multiuser environment, i.e., the degrees of freedom (DoF) is maximized [1]- [22]. The DoF has been adopted in informationtheoretic studies as the figure of merit that captures the prelog value of the capacity in high signal-to-noise ratio (SNR) regime.…”

“…Sridharan and Yu [18], [19] characterized the DoF of two-cell MIMO cellular networks as a piecewise linear function with either M or N being the bottleneck for both two-user-per-cell and three-user-per-cell cases, following insights from the subspace alignment approaches in [20], [21]. While several outer bounds and achievable schemes for the DoF in wireless cellular networks are known [12]- [19], [22], an exact characterization of the DoF for the case of arbitrary number of users in each cell remains unsolved. In this paper, we derive the achievable sum DoF for the uplink transmission of a two-cell multiuser MIMO interference network with T transmission time (channel extension) and arbitrary (possibly asymmetric) numbers of users in the two cells.…”