A new approach to beamformer design for massive MIMO systems based on k-Regularity

In this paper, a new beamformer design paradigm, named k-regular beamformer, is proposed for massive multiple-input multiple-output (MIMO) transmission systems to achieve most of the gain inherent to a large antenna array without too much complexity. In the proposed k-regular beamforming scheme, each of multiple data streams for MIMO transmission is multiplied by k complex gains and assigned to k out of available N_T transmit antennas, and signals assigned to the same transmit antenna are added and transmitted through the assigned antenna. The proposed k-regular beamformer can implement antenna selection (corresponding to k=1) to optimal eigen-beamforming (corresponding to k=N_T) by controlling the parameter k, and thus enables arbitrary trade-off between complexity and performance. Two beamformer design algorithms, the maximum correlation method (MCM) and the projected iterative shrinkage-thresholding algorithm (PISTA), are proposed to design k-regular beamforming matrices. Numerical results show that the proposed k-regular beamformer even with small k significantly improves the rate gain over simple antenna selection and achieves most of the optimal eigen-beamforming performance with far less complexity than that required for optimal eigen-beamforming for massive MIMO transmission.