Beamformer design for interference alignment using reweighted frobenius norm minimization

This paper proposes an algorithm to compute the uplink transmit beamformers for linear interference alignment in MIMO cellular networks without symbol extensions. In particular, we consider interference alignment in a network consisting of G cells and K users/cell, having N and M antennas at each base station (BS) and user respectively. Using an alternate interpretation of the conditions for interference alignment, we frame the problem of finding aligned transmit beamformers in the uplink as an optimization problem to minimize the rank of a set of interference matrices subject to affine constraints. The interference matrix of a BS consists of all the interfering vectors at that BS. The proposed algorithm approximates rank using the weighted Frobenius norm and iteratively updates the weights so that the weighted Frobenius norm is a close approximation of the rank of the interference matrix. A crucial aspect of this algorithm is the weight update rule that guides the algorithm towards aligned beamformers. We propose a novel weight update rule that discourages the algorithm from converging to local minima that do not generate the requisite number of interference free dimensions. The proposed algorithm is computationally efficient since it only requires solving a simple quadratic program in each iteration. Simulation results indicate much faster convergence to aligned beamformers when compared to algorithms of similar complexity.