Interference Alignment in Single-Beam MIMO Networks via Homotopy Continuation

TitleInterference Alignment in Single-Beam MIMO Networks via Homotopy Continuation
Publication TypeConference Paper
Year of Publication2011
AuthorsGonzález, Ó., and I. Santamaría
Conference NameIEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2011)
Month PublishedMay
Conference LocationPrague, Czech Republic
AbstractIn this paper we consider the application of a homotopy-continuation based method for finding interference alignment (IA) solutions for the deterministic K-user multiple-input multiple-output (MIMO) channel, when all users wish to send one stream of data. Homotopy continuation is based on the idea of deforming a start system, whose solution can easily be found, to reach the target system that we want to solve. For the IA problem we show that a good initial system is obtained by considering a rank-one approximation of the original MIMO interference channels. Specifically, as long as the original system is feasible, a rank-one approximation of the MIMO channels allow us to find a closed-form interference-free solution. The proposed algorithm is shown to have a lower complexity than previous methods with comparable sum-rate performance. Furthermore, it is also shown that the trivial system (rank-one MIMO channels) and target system (full-rank MIMO channels) have exactly the same number of solutions. Exploiting this equivalence, an efficient method to enumerate all the IA solutions that exist in a single-beam MIMO network is proposed.
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