Suchergebnisse

Alternating minimization and steepest descent are commonly used strategies to obtain interference alignment (IA) solutions in the K-user multiple-input multiple-output (MIMO) interference channel (IC). Although these algorithms are shown to converge monotonically, they experience a poor convergence rate, requiring an enormous amount of iterations which substantially increases with the size of the scenario. To alleviate this drawback, in this letter we resort to the Gauss-Newton (GN) method, which is well-known to experience quadratic convergence when the iterates are sufficiently close to the optimum. We discuss the convergence properties of the proposed GN algorithm and provide several numerical examples showing that it always converges to the optimum with quadratic rate, reducing dramatically the required computation time in comparison to other algorithms, hence paving a new way for the design of IA algorithms. ; The authors were supported by the Spanish Government (MICINN) under projects TEC2010-19545-C04-03 (COSIMA), CONSOLIDER-INGENIO 2010 CSD2008-00010 (COMONSENS) and FPU grants AP2009-1105 and AP2010-2189.

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. ; This work was supported by the Spanish Government, Ministerio de Ciencia e Innovación (MICINN), under project COSIMA (TEC2010-19545-C04-03), project COMONSENS (CSD2008-00010, CONSOLIDER-INGENIO 2010 Program) and FPU grant AP2009-1105.