An interference alignment algorithm for structured channels

In this paper we propose a new interference alignment (IA) algorithm specifically designed to work with structured channels (e.g., diagonal or block-diagonal). Multiple-input multiple-output (MIMO) structured channels arise when symbol extensions - either in time or frequency - are employed jointly with the spatial dimension in the design of the precoders. In this case, the rank constraint in the direct channels must explicitly be taken into account into the optimization problem to ensure that there is no degrees-of-freedom (DoF) loss. To this end, we propose an algorithm that minimizes the interference leakage while ensuring that the direct links are full rank and the transmitters satisfy a power constraint. The algorithm is based upon an alternating optimization procedure, which solves a generalized eigenvalue problem at each step. We show through simulations the advantages of the proposed algorithm in several scenarios that use symbols extensions or improper (a.k.a. asymmetric) signalling.