In this paper we propose an algorithm to design interference alignment (IA) precoding and decoding matrices for MIMO X networks (XN). The proposed algorithm is rooted in the homotopy continuation techniques commonly used to solve systems of nonlinear equations. Homotopy methods find the solution of a target system by smoothly deforming the known solutions of a start system which can be trivially solved. The key observation leading to a simple start system is realizing that the inverse IA problem, i.e., finding the channels that satisfy the IA conditions given a set of precoders and decoders, is linear and, therefore, a convenient trivial system. Once the start system has been solved, standard prediction and correction techniques are applied to track the solution all the way to the target system. Our results show that the proposed algorithm is able to consistently find solutions achieving the maximum number of degrees of freedom (DoF) whereas alternating minimization techniques, which typically work well for the interference channel (IC), repeatedly fail for the XN. Further, the algorithm provides insights into the feasibility of alignment in MIMO X networks for which theoretical results are scarce.Index Terms-Degrees of freedom, homotopy continuation, interference alignment, MIMO, X network.

Interference alignment (IA) has triggered high impact research in wireless communications since it was proposed nearly ten years ago. However, the vast majority of research are centered on the theory of IA and are hardly feasible in view of the existing state-of-the-art wireless technologies. Although several research groups assessed the feasibility of IA via testbed measurements in realistic environments, the experimental evaluation of IA is still in its infancy since most of the experiments were limited to simpler scenarios and configurations. This article summarizes the practical limitations of experimentally evaluating IA, provides an overview of the available IA testbed implementations, including the costs, and highlights the imperatives for the succeeding IA testbed implementations. Finally, the article explores future research directions on the applications of IA in the next generation wireless systems.

In this paper we present an experimental study on the performance of spatial Interference Alignment (IA) in broadband indoor wireless local area network scenarios that use Orthogonal Frequency Division Multiplexing (OFDM) according to the IEEE 802.11a physical-layer specifications. Experiments have been carried out using a wireless network testbed made up of six nodes equipped with Multiple-Input Multiple-Output (MIMO) radio interfaces. This setup allows the implementation of a 3-user MIMO interference channel. We have implemented different IA decoding schemes that operate either before or after the Fast Fourier Transform block. IA has been experimentally evaluated comparing both approaches to analyze its performance in synchronous and asynchronous transmissions. Our results indicate that spatial IA performs satisfactorily in practical broadband indoor scenarios in which wireless channels often exhibit relatively large coherence times.

In this paper, we propose an algorithm to maximize downlink rate performance in the context of multiple-input multiple-output (MIMO) Heterogeneous Networks (HetNets). Specifically, we evaluate the benefits of flexible duplexing, a promising strategy that consists in combining uplink and downlink cells within the same channel use. In order to handle intercell interference, we rely on the interference alignment (IA) technique, taking into account the impact of the channel estimation errors on the inter-cell interference leakage. Determining the best uplink/downlink configuration is a combinatorial problem, and therefore we consider several approaches to reduce the computational demands of the problem. First, we use a statistical characterization for the average rates achieved by IA in order to avoid the calculation of alignment solutions for all possible settings in the network. Additionally, we propose two hierarchical switching (HS) strategies so that only a subset among the total number of combinations is explored. As a performance baseline, we include in the comparison the conventional time division duplex (TDD) approach and the well-known minimum mean square error (MMSE) decoder. The obtained results show that downlink rates achieved by implementing flexible duplexing and applying inter-cell IA significantly outperform conventional TDD transmissions. Finally, the proposed hierarchical schemes are shown to obtain almost the same rates as exhaustive search with much lower computational cost.

In this paper we propose an algorithm to design interference alignment (IA) precoding and decoding matrices for arbitrary MIMO X networks. The proposed algorithm is rooted in the homotopy continuation techniques commonly used to solve systems of nonlinear equations. Homotopy methods find the solution of a target system by smoothly deforming the solution of a start system which can be trivially solved. Unlike previously proposed IA algorithms, the homotopy continuation technique allows us to solve the IA problem for both unstructured (i.e., generic) and structured channels such as those that arise when time or frequency symbol extensions are jointly employed with the spatial dimension. To this end, we consider an extended system of bilinear equations that include the standard alignment equations to cancel the interference, and a new set of bilinear equations that preserve the desired dimensionality of the signal spaces at the intended receivers. We propose a simple method to obtain the start system by randomly choosing a set of precoders and decoders, and then finding a set of channels satisfying the system equations, which is a linear problem. Once the start system is available, standard prediction and correction techniques are applied to track the solution all the way to the target system. We analyze the convergence of the proposed algorithm and prove that, for many feasible systems and a sufficiently small continuation parameter, the algorithm converges with probability one to a perfect IA solution. The simulation results show that the proposed algorithm is able to consistently find solutions achieving the maximum number of degrees of freedom (DoF) in a variety of MIMO X networks with or without symbol extensions. Further, the algorithm provides insights into the feasibility of IA in MIMO X networks for which theoretical results are scarce.