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.