Enabling Decentralized Computation of the WAX Decomposition

As the number of antennas scales up, research efforts have been directed towards finding decentralized receiver solutions for multi-antenna architectures. In a recent paper, a novel matrix decomposition - the WAX decomposition was proposed, which has direct bearing on characterizing the level of decentralization that is possible if the complexity of the decentralized processing is limited. However, the available work on WAX decomposition has left some gaps in determining how one of its basis matrices has to be defined. In this paper we present a number of constructions for effectively defining said basis matrix, and we show how they facilitate decentralized calculation of the WAX decomposition itself for applying information-lossless processing in architectures with an arbitrary level of decentralization. Thereby, taking a major step towards realizing decentralized receiver solution for large scale antenna systems.