Subspace optimisation-based iterative interference alignment algorithm on the grassmann manifold

An iterative interference alignment (IA) algorithm for the multi-user multi-input multi-output interference channel is proposed, which optimises on the Grassmann manifold to improve the performance of conventional interference subspace (ISS) alignment algorithm without the assumption of channel reciprocity. The proposed algorithm combines the extreme eigenvalues method and the modified steepest descent method on the Grassmann manifold to minimise the distances not only between the ISS and the subspace spanned by interference, but also between the desired signal subspace and the subspace spanned by useful signal. Utilising the subspace optimisation above, both the interference and useful signal are aligned to their respective subspaces. Numerical results show that the proposed algorithm can significantly improve the sum rate of interference channel. Moreover, by properly choosing the attenuation factor of step size, the proposed algorithm can achieve an effective tradeoff between sum rate performance and convergence speed, which gives the IA scheme more design flexibility.