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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.

The localization problem in a wireless sensor network is to determine the coordination of sensor nodes using the known positions of some nodes (called anchors) and corresponding noisy distance measurements. There is a variety of different approaches to solve this problem such as semi-definite programming (SDP) based, sum of squares and second order cone programming, and between them, SDP-based approaches have shown good performance. In recent years, the primary SDP approach has been investigated and a variety of approaches are proposed in order to enhance its performance. In SDP approaches, errors in approximating the given distances are minimized as an objective function. It is desirable that the distribution of error in these problems would be a delta distribution, which is practically impossible. Therefore, we may approximate delta distribution by Gaussian distribution with very small variance. In this paper, we define a new objective function which makes the error distribution as similar as possible to a Gaussian distribution with a very small variance. Simulation results show that our proposed method has higher accuracy compared to the traditional SDP approach and other prevalent objective functions which are used such as least squares. Our method is also faster than other popular approaches which try to improve the accuracy of the primary SDP approach., Comment: 11 pages, 9 figures