Asymmetric signal space alignment for multi-pair two-way relaying network

In this paper, we investigate asymmetric signal space alignment (ASSA) for the multi-pair two-way relaying (TWR) network, which consists of three pairs of single-antenna users and a two-antenna common access relay. In this particular scenario, the traditional signal space alignment (SSA) scheme has to rely on symbol extension for the reason of insufficient spatial dimensions. Moreover, the naive zero-forcing (ZF) based scheme only achieves 1 degrees of freedom (DOF). By utilizing ASSA, the DOF of 1.5 can be obtained without symbol extension. In addition, in order to further improve the sum rate, a joint beamforming optimization (JBO) algorithm is presented, which jointly optimizes the beam vectors of the users and relay. In consideration of the case with more than three pairs of users, we also propose a semi-orthogonal aligned user-pair scheduling (SAUS) method, which not only facilitates the ASSA scheme, but also harvests the multiuser diversity (MuD) to enhance the performance.