Paper accepted in IEEE Transactions on Signal Processing

The paper "Homotopy Continuation for Spatial Interference Alignment in Arbitrary MIMO X Networks", co-authored by J. Fanjul, O. Gonzalez, I. Santamaría and C. Beltran, has been accepted for publication in the IEEE Transactions on Signal Processing.

Abstract: In this paper we have presented a new algorithm, based on homotopy continuation, to design interference alignment precoders and decoders for MIMO X networks. The rank constraints on the direct channels are explicitly taken into account and reformulated as new bilinear equations to be solved by the homotopy continuation method together with the conventional interference alignment equations. In this way, the proposed method is able to provide perfect alignment solutions even when time or frequency symbol extensions are used. Unlike competing algorithms, the proposed method has provable convergence guarantees when the IA problem is feasible. Moreover, the proposed algorithm outperforms other existing algorithms, such as the well-known alternating minimization scheme, for a wide variety of channel models including the IC, IBC and IMAC cellular networks, and the X-channel. Finally, the proposed technique has allowed us to provide some insights into the potential benefits of the reverse TDD configuration in comparison to the conventional IMAC and IBC cellular topologies.