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Interference alignment (IA) is a key technology for achieving the capacity scaling required by next generation wireless networks, which is proved to obtain the maximum degrees of freedom (DoF). The aim of this paper is to propose interference alignment schemes through manifold optimization theory for K-user interference channel. We limit the optimization only at transmitters and relax the hypothesis of channel reciprocity to mitigate the overhead caused by alternation between the forward and reverse links significantly. Firstly, we introduce a classical algorithm based on the steepest descent (SD) algorithm in a multi-dimensional complex space to achieve feasible IA. Then, we reform the optimization problem on Stiefel manifold and propose a novel SD algorithm based on this manifold with lower dimensions. Moreover, aiming at further reducing the complexity, the Grassmann manifold is introduced to derive corresponding algorithm for reaching the perfect IA. Numerical simulations show that the proposed algorithms on manifolds have better performance both on system throughput and convergence than classical methods and also achieve the maximum DoF.

Interference alignment schemes for k-user interference channel based on manifold optimization