Gradient projection based interference alignment for the MIMO X channel

We regard a MIMO network with two transmitters and two receivers, in which each transmitter sends information to both of the receivers, a scenario known as the MIMO X channel. For such a system, the recently proposed interference alignment technique is proven to achieve the maximum degrees of freedom, which cannot be reached by conventional zero-forcing. In contrast to other scenarios, for the MIMO X channel algebraic expressions to obtain interference alignment can be easily found. Additionally, the set of parameters for possible alignments is a continuous manifold rather than a discrete set, which directly raises the question of how to find the best alignment when aiming at maximizing a utility of the transmission rates. Due to the non-convexity of the problem, finding the global optimally solution is numerically exhaustive and we are willing to accept a locally optimal solution. In this work we show an efficient parametrization of the problem which allows to apply a projected gradient approach that guarantees an aligned solution. In numerical simulations we show the superiority of our method compared to existing algorithms.