Widely linear Interference Alignment precoding

Interference Alignment is an intriguing approach to the development of interference management schemes for wireless networks. Even for networks of single antenna nodes with time-invariant channels, several approaches to interference alignment have been proposed. Those schemes construct transmitted signals that are not circularly symmetric by using symbols from real-valued constellations. In this paper we develop an alternative scheme that employs widely linear precoding of symbols from conventional complex-valued constellations at the transmitters, and a periodic conjugation operation at the receivers. Like the existing schemes, the proposed scheme achieves the degrees of freedom of the channel, and it adds the convenience of enabling the use of conventional constellations. To tackle the difficult problem of optimizing the sum rate under the interference alignment constraint, we develop an efficient algorithm on the Grassmannian manifold, and we demonstrate that this algorithm can reduce the power offset and hence provide significant increases in the sum rate at low to moderate SNRs.