Perfect versus imperfect interference alignment using multiple MIMO relays

Interference alignment is a promising approach to handle the interference in mobile radio networks especially at high SNR. In the present paper, the interference alignment is achieved using a number of MIMO relays in a scenario with K single antenna node pairs. A two-phase transmission scheme is considered assuming the channel to be constant during the transmission phases. Firstly, the source nodes transmit to both the relays and the destination nodes. Secondly, the source nodes and the relays retransmit to the destination nodes. By adapting the relays' processing matrices to the channel while fixing the nodes' filters, a linear system of equations is formulated which is solved for the interference alignment. The interference signals can be aligned perfectly at the destination nodes if there are enough relays. A closed-form solution with minimum retransmit energy at the relays is selected if the linear system of equations is under-determined. If the system of linear equations has no solution, i.e., if there are not enough relays, least squares based solutions are employed which minimize the total received interference. The results show that K/2 degrees of freedom are achieved if the interference signals are aligned perfectly. Furthermore, aligning the interference signals imperfectly achieves a capacity-gain over perfect interference alignment at low and moderate SNRs while requiring a lower number of relays.