Optimization of Interference Alignment Beamforming Vectors

The K user interference alignment scheme proposed by Cadambe and Jafar (CJ) achieves K/2 degrees of freedom for networks with frequency selective channels. In this paper, we provide two new algorithms that optimize the precoding subspaces which maximize the data rate performance of the CJ scheme while maintaining the achievable degrees of freedom. One design is obtained as a global solution of a constrained convex (concave) optimization problem that maximizes the sum rate. The other design provides a low complexity closed-form solution to a constrained maximization problem with a suboptimal sum rate objective function. We also show that both designs can be combined with Shen, Host-Madsen and Vidal orthonormalization that achieves further gains in sum rate by optimizing the precoding vectors generated by the proposed algorithms.