Asymmetric signal space alignment for Y channel with single-antenna users

In this paper, we study the amplify-and-forward (AF) relaying based signaling scheme for the Y channel consisting of three single-antenna users and a two-antenna relay. In such a particular scenario, traditional signal space alignment for network coding (SSA-NC) scheme is not feasible. Moreover, the time division based multi-user multiple-input multiple-output (MU-MIMO) scheme has to rely on time division mode, i.e., more than two time slots are required to complete the whole communication process, which results in throughput loss. We develop an asymmetric signal space alignment (ASSA) scheme to enable all the users to finish information exchange with each other via the relay within two time slots. Brief degrees of freedom (DOF) analysis and numerical simulations have been provided to demonstrate that the proposed signaling technique significantly outperforms the conventional time division based MU-MIMO scheme.