  Nowadays, providing higher data rate is a momentous goal for wireless
communications systems. Interference is one of the important obstacles to reach
this purpose. Interference alignment is a management technique that align
interference from other transmitters in the least possible dimension subspace
at each receiver and as a result, provide the remaining dimensions for free
interference signal. An uncoordinated interference is an example of
interference which cannot be aligned coordinately with interference from
coordinated part and consequently, the performance of interference alignment
approaches is degraded. In this paper, we propose two rank minimization methods
to enhance the performance of interference alignment in the presence of
uncoordinated interference sources. Firstly, a new objective function is chosen
then, a new class of convex relaxation is proposed with respect to the
uncoordinated interference which leads to decrease the optimal value of our
optimization problem. Moreover, we use schatten-p-norm as surrogate of rank
function and we implement iteratively reweighted algorithm to solve
optimization problem. In addition, we apply our proposed methods to mitigate
interference in relay-aided MIMO interference channel, and propose a
weighted-sum method to improve the performance of interference alignment in the
amplify-and-forward relay-aided MIMO system based on the rank minimization
approach. Finally, our simulation results show that our proposed methods can
obtain considerably higher multiplexing gain and sum rate than other approaches
in the interference alignment framework and the performance of interference
alignment is improved.
